## Fuchs, Martin

Compute Distance To:
 Author ID: fuchs.martin Published as: Fuchs, Martin; Fuchs, M. Homepage: http://www.math.uni-sb.de/ag/fuchs/Menupkte/Arbeitsgruppe/fuchs.html External Links: MGP · Math-Net.Ru
 Documents Indexed: 175 Publications since 1983, including 3 Books 1 Contribution as Editor Reviewing Activity: 166 Reviews Co-Authors: 24 Co-Authors with 121 Joint Publications 544 Co-Co-Authors
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### Co-Authors

 51 single-authored 67 Bildhauer, Michael 12 Duzaar, Frank 12 Seregin, Gregory A. 8 Müller, Jan-Steffen 8 Repin, Sergeĭ Igorevich 6 Zhong, Xiao 5 Tietz, Christian 4 Apushkinskaya, Darya E. 4 Li, Gongbao 4 Reuling, Jürgen 4 Weickert, Joachim 3 Osmolovskij, V. G. 3 Zhang, Guo 2 Breit, Dominic 2 Elfanni, Abdellah 2 Mingione, Giuseppe 1 Alber, Hans-Dieter 1 Cárdenas, Marcelo 1 Diening, Lars 1 Fusco, Nicola 1 Grotowski, Joseph F. 1 Martio, Olli 1 Mockett, Charles 1 Scheffler, Matthias 1 Schirra, Oliver D. 1 Thiele, Frank 1 Wiegner, Michael
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### Serials

 24 Journal of Mathematical Sciences (New York) 14 Manuscripta Mathematica 10 Mathematical Methods in the Applied Sciences 8 Calculus of Variations and Partial Differential Equations 8 St. Petersburg Mathematical Journal 8 Journal of Mathematical Fluid Mechanics 7 Commentationes Mathematicae Universitatis Carolinae 7 Zeitschrift für Analysis und ihre Anwendungen 6 Archiv der Mathematik 5 Analysis 5 Asymptotic Analysis 5 Annales Academiae Scientiarum Fennicae. Mathematica 4 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Mathematische Nachrichten 2 Journal of Mathematical Analysis and Applications 2 Mathematische Zeitschrift 2 Numerical Functional Analysis and Optimization 2 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 2 Communications in Partial Differential Equations 2 Irish Mathematical Society Bulletin 2 Bollettino della Unione Matemàtica Italiana. Serie VII. A 2 Bollettino della Unione Matemàtica Italiana. Serie VII. B 2 Journal of Convex Analysis 2 Journal of Applied Analysis 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Acta Mathematica Scientia. Series B. (English Edition) 1 Applicable Analysis 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Applied Mathematics and Optimization 1 Journal of Differential Equations 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matematico della Università di Padova 1 Ricerche di Matematica 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Algebra i Analiz 1 The Journal of Geometric Analysis 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Non-Newtonian Fluid Mechanics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Acta Mathematica Scientia 1 Advances in Mathematical Sciences and Applications 1 Annales Universitatis Saraviensis. Series Mathematicae 1 NoDEA. Nonlinear Differential Equations and Applications 1 Abstract and Applied Analysis 1 Applied Mathematics E-Notes 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Complex Variables and Elliptic Equations 1 Bonner Mathematische Schriften 1 Lecture Notes in Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Journal of Elliptic and Parabolic Equations 1 Annales Fennici Mathematici
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### Fields

 118 Calculus of variations and optimal control; optimization (49-XX) 81 Partial differential equations (35-XX) 35 Mechanics of deformable solids (74-XX) 32 Fluid mechanics (76-XX) 15 Global analysis, analysis on manifolds (58-XX) 13 Information and communication theory, circuits (94-XX) 10 Differential geometry (53-XX) 8 Functional analysis (46-XX) 7 Real functions (26-XX) 7 Numerical analysis (65-XX) 7 Computer science (68-XX) 2 Potential theory (31-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

147 Publications have been cited 1,259 times in 561 Documents Cited by Year
Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Zbl 0964.76003
Fuchs, Martin; Seregin, Gregory
2000
Full $$C^{1,\alpha}$$-regularity for free and constrained local minimizers of elliptic variational integrals with nearly linear growth. Zbl 0995.49023
Fuchs, Martin; Mingione, Giuseppe
2000
$$C^{1,\alpha}$$-solutions to non-autonomous anisotropic variational problems. Zbl 1101.49029
Bildhauer, Michael; Fuchs, Martin
2005
A regularity theory for variational integrals with $$L\ln L$$-growth. Zbl 0929.49022
Fuchs, Martin; Seregin, Gregory
1998
Variational integrals on Orlicz-Sobolev spaces. Zbl 0913.49023
Fuchs, M.; Osmolovski, V.
1998
p-harmonic obstacle problems. I: Partial regularity theory. Zbl 0715.49003
Fuchs, Martin
1990
Partial regularity for variational integrals with $$(s,\mu,q)$$-growth. Zbl 1018.49026
Bildhauer, Michael; Fuchs, Martin
2001
Variational inequalities for energy functionals with nonstandard growth conditions. Zbl 0987.49019
Fuchs, Martin; Li, Gongbao
1998
Steady states of anisotropic generalized Newtonian fluids. Zbl 1162.76375
Apushkinskaya, Darya; Bildhauer, Michael; Fuchs, Martin
2005
On removable singularities of p-harmonic maps. Zbl 0715.49040
Duzaar, F.; Fuchs, M.
1990
Solenoidal Lipschitz truncation and applications in fluid mechanics. Zbl 1245.35080
Breit, D.; Diening, L.; Fuchs, M.
2012
Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening. Zbl 0928.76087
Fuchs, Martin; Seregin, Gregory
1999
A lemma on the higher integrability of functions with applications to the regularity theory of two-dimensional generalized Newtonian fluids. Zbl 1116.49018
Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao
2005
A variational approach to the denoising of images based on different variants of the TV-regularization. Zbl 1260.49074
Bildhauer, Michael; Fuchs, Martin
2012
Variants of the Stokes problem: the case of anisotropic potentials. Zbl 1072.76019
Bildhauer, Michael; Fuchs, Martin
2003
The nonlinear Stokes problem with general potentials having superquadratic growth. Zbl 1270.35335
Breit, Dominic; Fuchs, Martin
2011
Hölder continuity of the gradient for degenerate variational inequalities. Zbl 0701.49019
Fuchs, Martin
1990
On a class of variational integrals with linear growth satisfying the condition of $$\mu$$-ellipticity. Zbl 1047.49029
Bildhauer, Michael; Fuchs, Martin
2002
The Green matrix for strongly elliptic systems of second order with continuous coefficients. Zbl 0634.35023
Fuchs, M.
1986
Optimal regularity theorems for variational problems with obstacles. Zbl 0605.49006
Duzaar, F.; Fuchs, M.
1986
The blow-up of $$p$$-harmonic maps. Zbl 0794.58012
Fuchs, Martin
1993
Some remarks on the boundary regularity for minima of variational problems with obstacles. Zbl 0587.49011
Fuchs, Martin
1986
Variational inequalities for vector-valued functions with non-convex obstacles. Zbl 0589.35049
Fuchs, Martin
1985
Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals. Zbl 1120.49031
Bildhauer, M.; Fuchs, M.
2007
A priori gradient bounds and local $$C^{1,\alpha}$$-estimates for (double) obstacle problems under non-standard growth conditions. Zbl 1011.49024
Bildhauer, M.; Fuchs, M.; Mingione, G.
2001
On some perturbations of the total variation image inpainting method. I: Regularity theory. Zbl 1321.49060
Bildhauer, M.; Fuchs, M.
2014
Regularity results for the quasi-static Bingham variational inequality in dimensions two and three. Zbl 0899.76044
Fuchs, Martin; Seregin, Gregory
1998
Partial regularity for a class of anisotropic variational integrals with convex hull property. Zbl 1076.49018
Bildhauer, M.; Fuchs, M.
2002
On some perturbations of the total variation image inpainting method. II: Relaxation and dual variational formulation. Zbl 1321.49054
Bildhauer, M.; Fuchs, M.
2015
Variational problems with non-convex obstacles and an integral constraint for vector-valued functions. Zbl 0568.49009
Duzaar, Frank; Fuchs, Martin
1986
Stationary flows of shear thickening fluids in 2D. Zbl 1294.35097
Fuchs, Martin
2012
On stationary incompressible Norton fluids and some extensions of Korn’s inequality. Zbl 0812.76007
Fuchs, Martin
1994
A regularity theory for scalar local minimizers of splitting-type variational integrals. Zbl 1150.49015
Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao
2007
A regularity result for stationary electrorheological fluids in two dimensions. Zbl 1058.76073
Bildhauer, Michael; Fuchs, Martin
2004
Korn inequalities in Orlicz spaces. Zbl 1237.26013
Fuchs, Martin
2010
Liouville theorems for stationary flows of shear thickening fluids in the plane. Zbl 1254.76055
Fuchs, Martin
2012
Liouville-type theorems for steady flows of degenerate power law fluids in the plane. Zbl 1273.76076
Bildhauer, Michael; Fuchs, Martin; Zhang, Guo
2013
Local Lipschitz regularity of vector valued local minimizers of variational integrals with densities depending on the modulus of the gradient. Zbl 1211.49047
Fuchs, Martin
2011
Interior gradient bounds for local minimizers of variational integrals under nonstandard growth conditions. Zbl 1357.49010
Apushkinskaya, D.; Bildhauer, M.; Fuchs, M.
2010
Topics in the calculus of variations. Zbl 0834.49019
Fuchs, Martin
1994
Non-linear elliptic systems involving measure data. Zbl 0838.35133
Fuchs, M.; Reuling, J.
1995
Some remarks on non-Newtonian fluids including nonconvex perturbations of the Bingham and Powell-Eyring model for viscoplastic fluids. Zbl 0882.76007
Fuchs, Martin; Seregin, Gregory
1997
Partial regularity results for vector valued functions which minimize certain functionals having non quadratic growth under smooth side conditions. Zbl 0642.49002
Fuchs, Martin; Fusco, Nicola
1988
Relaxation of convex variational problems with linear growth defined on classes of vector-valued functions. Zbl 1029.49013
Bildhauer, M.; Fuchs, M.
2003
Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials. Zbl 1189.49057
Bildhauer, Michael; Fuchs, Martin
2010
Existence of generalized minimizers and dual solutions for a class of variational problems with linear growth related to image recovery. Zbl 1331.49014
Fuchs, M.; Tietz, C.
2015
A posteriori error estimates of functional type for variational problems related to generalized Newtonian fluids. Zbl 1105.76049
Fuchs, M.; Repin, S.
2006
On the existence of integral currents with prescribed mean curvature vector. Zbl 0703.49035
Duzaar, Frank; Fuchs, Martin
1990
An application of a new coercive inequality to variational problems studied in general relativity and in Cosserat elasticity giving the smoothness of minimizers. Zbl 1180.49040
Fuchs, Martin; Schirra, Oliver
2009
On variational models for quasi-static Bingham fluids. Zbl 0857.76006
Fuchs, Martin; Grotowski, Joseph F.; Reuling, Jürgen
1996
On quasi-static non-Newtonian fluids with power-law. Zbl 0858.76006
Fuchs, Martin
1996
Hölder continuity for weak extremals of some two-dimensional variational problems related to nonlinear elasticity. Zbl 0929.49021
Fuchs, Martin; Seregin, Gregori
1997
Regularity theorems for nonlinear systems of partial differential equations under natural ellipticity conditions. Zbl 0624.35032
Fuchs, Martin
1987
Twodimensional anisotropic variational problems. Zbl 1026.49027
Bildhauer, M.; Fuchs, M.
2003
Variational integrals of splitting-type: higher integrability under general growth conditions. Zbl 1181.49035
Bildhauer, M.; Fuchs, M.
2009
p-harmonic obstacle problems. III: Boundary regularity. Zbl 0715.49005
Fuchs, M.
1990
Liouville theorems for entire local minimizers of energies defined on the class $$L \log L$$ and for entire solutions of the stationary Prandtl-Eyring fluid model. Zbl 1252.49075
Fuchs, Martin; Zhang, Guo
2012
$$C^{1,\alpha}$$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting. Zbl 1335.49058
Bildhauer, M.; Fuchs, M.; Tietz, C.
2016
Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity. Zbl 0827.73009
Fuchs, Martin; Reuling, Jürgen
1995
A regularity theorem for energy minimizing maps of Riemannian manifolds. Zbl 0619.58019
Fuchs, Martin
1987
The Green-matrix for elliptic systems which satisfy the Legendre-Hadamard condition. Zbl 0552.35025
Fuchs, Martin
1984
A note on non-uniformly elliptic Stokes-type systems in two variables. Zbl 1195.76148
Fuchs, Martin
2010
p-harmonic obstacle problems. II: Extensions of maps and applications. Zbl 0715.49004
Fuchs, Martin
1989
Some regularity theorems for mappings which are stationary points of the p-energy functional. Zbl 0683.49014
Fuchs, Martin
1989
Signal recovery via TV-type energies. Zbl 1392.49003
Fuchs, M.; Müller, J.; Tietz, C.
2018
Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth. Zbl 0977.49025
Bildhauer, M.; Fuchs, M.
1999
Existence and regularity of functions which minimize certain energies in homotopy classes of mappings. Zbl 0771.49016
Duzaar, Frank; Fuchs, Martin
1991
Partial regularity for local minimizers of splitting-type variational integrals. Zbl 1141.49032
Bildhauer, M.; Fuchs, M.
2007
A general existence theorem for integral currents with prescribed mean curvature form. Zbl 0786.49025
Duzaar, Frank; Fuchs, Martin
1992
Partial regularity of the deformation gradient for some model problems in nonlinear two-dimensional elasticity. Zbl 0827.73010
Fuchs, M.; Seregin, G.
1994
Lipschitz regularity for certain problems from relaxation. Zbl 0883.49028
Fuchs, Martin
1996
On integral currents with constant mean curvature. Zbl 0739.49026
Duzaar, Frank; Fuchs, Martin
1991
Denoising and inpainting of images using TV-type energies: theoretical and computational aspects. Zbl 1381.94011
Bildhauer, M.; Fuchs, M.; Weickert, J.
2016
Regularity for a class of variational integrals motivated by nonlinear elasticity. Zbl 0809.49010
Fuchs, Martin
1994
Einige Bemerkungen über die Regularität von stationären Punkten gewisser geometrischer Variationsintegrale. (Some remarks on the regularity of stationary points of certain geometrical variational integrals). Zbl 0758.35017
Duzaar, Frank; Fuchs, Martin
1991
A posteriori error estimates for the approximations of the stresses in the Hencky plasticity problem. Zbl 1419.74076
Fuchs, M.; Repin, S.
2011
Estimates of the deviations from the exact solutions for variational inequalities describing the stationary flow of certain viscous incompressible fluids. Zbl 1357.76062
Fuchs, M.; Repin, S.
2010
A posteriori error estimates for stationary slow flows of power-law fluids. Zbl 1109.76007
Bildhauer, M.; Fuchs, M.; Repin, S.
2007
A higher order TV-type variational problem related to the denoising and inpainting of images. Zbl 1358.49043
Fuchs, Martin; Müller, Jan
2017
Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Zbl 0998.81551
Fuchs, Martin; Scheffler, Matthias
1999
A note on a Liouville type result of Gilbarg and Weinberger for the stationary Navier-Stokes equations in 2D. Zbl 1291.35218
Fuchs, M.; Zhong, X.
2011
Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Zbl 0943.74076
Fuchs, Martin; Seregin, Gregory
1999
Global gradient bounds for relaxed variational problems. Zbl 0892.49027
Fuchs, Martin; Li, Gongbao
1997
An elementary partial regularity proof for vector-valued obstacle problems. Zbl 0609.35011
Fuchs, Martin
1987
The regularity of minima of variational problems with graph obstacles. Zbl 0644.49008
Fuchs, Martin; Wiegner, Michael
1989
A note on removable singularities for minima of certain vector-valued obstacle problems. Zbl 0608.49006
Fuchs, Martin
1987
$$L^\infty$$-bounds for elliptic equations on Orlicz-Sobolev spaces. Zbl 0933.35053
Fuchs, Martin; Li, Gongbao
1999
A global nonlinear evolution problem for generalized Newtonian fluids: Local initial regularity of the strong solution. Zbl 1122.76008
Fuchs, M.; Seregin, G.
2007
Computable upper bounds for the constants in Poincaré-type inequalities for fields of bounded deformation. Zbl 1403.74017
Fuchs, Martin
2011
The smoothness of the free boundary for a class of vector-valued problems. Zbl 0694.35220
Fuchs, Martin
1989
Image inpainting with energies of linear growth. A collection of proposals. Zbl 1302.49004
Bildhauer, M.; Fuchs, M.
2014
A geometric maximum principle for variational problems in spaces of vector-valued functions of bounded variation. Zbl 1319.49074
Bildhauer, Michael; Fuchs, Martin
2011
Generalizations of Korn’s inequality based on gradient estimates in Orlicz spaces and applications to variational problems in 2D involving the trace free part of the symmetric gradient. Zbl 1286.49042
Fuchs, M.
2010
Higher order variational problems on two-dimensional domains. Zbl 1136.49027
Bildhauer, Michael; Fuchs, Martin
2006
An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions. Zbl 1276.31001
Fuchs, Martin
2011
The elastic-plastic torsion problem: A posteriori error estimates for approximate solutions. Zbl 1172.74033
Bildhauer, M.; Fuchs, M.; Repin, S.
2009
Partial regularity of the deformation gradient for some model problems in nonlinear two-dimensional elasticity. Zbl 0839.73009
Fuchs, M.; Seregin, G.
1994
Higher order variational inequalities with non-standard growth conditions in dimension two: plates with obstacles. Zbl 1014.49031
Bildhauer, Michael; Fuchs, Martin
2001
Convex variational problems with linear growth. Zbl 1046.35020
Bildhauer, Michael; Fuchs, Martin
2003
Compact embeddings of the space of functions with bounded logarithmic deformation. Zbl 1229.46023
Fuchs, M.; Bildhauer, M.
2011
Some geometric properties of nonparametric $$\mu$$-surfaces in $$\mathbb{R}^3$$. Zbl 1482.49047
Bildhauer, Michael; Fuchs, Martin
2022
Liouville-type results in two dimensions for stationary points of functionals with linear growth. Zbl 1485.49016
Bildhauer, Michael; Fuchs, Martin
2022
On a class of variational problems with linear growth and radial symmetry. Zbl 07442495
Bildhauer, Michael; Fuchs, Martin
2021
Splitting type variational problems with linear growth conditions. Zbl 1448.49011
Bildhauer, M.; Fuchs, M.
2020
Signal recovery via TV-type energies. Zbl 1392.49003
Fuchs, M.; Müller, J.; Tietz, C.
2018
A remark on denoising of greyscale images using energy densities with varying growth rates. Zbl 1398.49032
Fuchs, M.; Müller, J.
2018
Existence and regularity for stationary incompressible flows with dissipative potentials of linear growth. Zbl 1404.76011
Bildhauer, M.; Fuchs, M.; Müller, J.
2018
A higher order TV-type variational problem related to the denoising and inpainting of images. Zbl 1358.49043
Fuchs, Martin; Müller, Jan
2017
An alternative approach towards the higher order denoising of images. analytical aspects. Zbl 1384.35019
Bildhauer, M.; Fuchs, M.; Weickert, J.
2017
$$C^{1,\alpha}$$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting. Zbl 1335.49058
Bildhauer, M.; Fuchs, M.; Tietz, C.
2016
Denoising and inpainting of images using TV-type energies: theoretical and computational aspects. Zbl 1381.94011
Bildhauer, M.; Fuchs, M.; Weickert, J.
2016
On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case. Zbl 1382.49044
Bildhauer, M.; Fuchs, M.; Müller, J.; Tietz, C.
2016
On some perturbations of the total variation image inpainting method. II: Relaxation and dual variational formulation. Zbl 1321.49054
Bildhauer, M.; Fuchs, M.
2015
Existence of generalized minimizers and dual solutions for a class of variational problems with linear growth related to image recovery. Zbl 1331.49014
Fuchs, M.; Tietz, C.
2015
On some perturbations of the total variation image inpainting method. III: Minimization among sets with finite perimeter. Zbl 1335.49024
Bildhauer, M.; Fuchs, M.
2015
On some perturbations of the total variation image inpainting method. I: Regularity theory. Zbl 1321.49060
Bildhauer, M.; Fuchs, M.
2014
Image inpainting with energies of linear growth. A collection of proposals. Zbl 1302.49004
Bildhauer, M.; Fuchs, M.
2014
Variations on Liouville’s theorem in the setting of stationary flows of generalized Newtonian fluids in the plane. Zbl 1311.35216
Fuchs, M.
2014
Liouville-type theorems for steady flows of degenerate power law fluids in the plane. Zbl 1273.76076
Bildhauer, Michael; Fuchs, Martin; Zhang, Guo
2013
Solenoidal Lipschitz truncation and applications in fluid mechanics. Zbl 1245.35080
Breit, D.; Diening, L.; Fuchs, M.
2012
A variational approach to the denoising of images based on different variants of the TV-regularization. Zbl 1260.49074
Bildhauer, Michael; Fuchs, Martin
2012
Stationary flows of shear thickening fluids in 2D. Zbl 1294.35097
Fuchs, Martin
2012
Liouville theorems for stationary flows of shear thickening fluids in the plane. Zbl 1254.76055
Fuchs, Martin
2012
Liouville theorems for entire local minimizers of energies defined on the class $$L \log L$$ and for entire solutions of the stationary Prandtl-Eyring fluid model. Zbl 1252.49075
Fuchs, Martin; Zhang, Guo
2012
Progress in DES for wall-modelled LES of complex internal flows. Zbl 1365.76093
Mockett, C.; Fuchs, M.; Thiele, F.
2012
The nonlinear Stokes problem with general potentials having superquadratic growth. Zbl 1270.35335
Breit, Dominic; Fuchs, Martin
2011
Local Lipschitz regularity of vector valued local minimizers of variational integrals with densities depending on the modulus of the gradient. Zbl 1211.49047
Fuchs, Martin
2011
A posteriori error estimates for the approximations of the stresses in the Hencky plasticity problem. Zbl 1419.74076
Fuchs, M.; Repin, S.
2011
A note on a Liouville type result of Gilbarg and Weinberger for the stationary Navier-Stokes equations in 2D. Zbl 1291.35218
Fuchs, M.; Zhong, X.
2011
Computable upper bounds for the constants in Poincaré-type inequalities for fields of bounded deformation. Zbl 1403.74017
Fuchs, Martin
2011
A geometric maximum principle for variational problems in spaces of vector-valued functions of bounded variation. Zbl 1319.49074
Bildhauer, Michael; Fuchs, Martin
2011
An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions. Zbl 1276.31001
Fuchs, Martin
2011
Compact embeddings of the space of functions with bounded logarithmic deformation. Zbl 1229.46023
Fuchs, M.; Bildhauer, M.
2011
Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient. Zbl 1305.74038
Fuchs, M.; Repin, S.
2011
Korn inequalities in Orlicz spaces. Zbl 1237.26013
Fuchs, Martin
2010
Interior gradient bounds for local minimizers of variational integrals under nonstandard growth conditions. Zbl 1357.49010
Apushkinskaya, D.; Bildhauer, M.; Fuchs, M.
2010
Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials. Zbl 1189.49057
Bildhauer, Michael; Fuchs, Martin
2010
A note on non-uniformly elliptic Stokes-type systems in two variables. Zbl 1195.76148
Fuchs, Martin
2010
Estimates of the deviations from the exact solutions for variational inequalities describing the stationary flow of certain viscous incompressible fluids. Zbl 1357.76062
Fuchs, M.; Repin, S.
2010
Generalizations of Korn’s inequality based on gradient estimates in Orlicz spaces and applications to variational problems in 2D involving the trace free part of the symmetric gradient. Zbl 1286.49042
Fuchs, M.
2010
Regularity results for local minimizers of energies with general densities having superquadratic growth. Zbl 1207.49046
Fuchs, M.
2010
On local generalized minimizers and local stress tensors for variational problems with linear growth. Zbl 1301.49096
Apushkinskaya, D.; Bildhauer, M.; Fuchs, M.
2010
An application of a new coercive inequality to variational problems studied in general relativity and in Cosserat elasticity giving the smoothness of minimizers. Zbl 1180.49040
Fuchs, Martin; Schirra, Oliver
2009
Variational integrals of splitting-type: higher integrability under general growth conditions. Zbl 1181.49035
Bildhauer, M.; Fuchs, M.
2009
The elastic-plastic torsion problem: A posteriori error estimates for approximate solutions. Zbl 1172.74033
Bildhauer, M.; Fuchs, M.; Repin, S.
2009
Minimization of energies related to the plate problem. Zbl 1159.74022
Fuchs, M.
2009
Duality based a posteriori error estimates for higher order variational inequalities with power growth functionals. Zbl 1151.65057
Bildhauer, Michael; Fuchs, Martin; Repin, Sergey
2008
Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals. Zbl 1120.49031
Bildhauer, M.; Fuchs, M.
2007
A regularity theory for scalar local minimizers of splitting-type variational integrals. Zbl 1150.49015
Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao
2007
Partial regularity for local minimizers of splitting-type variational integrals. Zbl 1141.49032
Bildhauer, M.; Fuchs, M.
2007
A posteriori error estimates for stationary slow flows of power-law fluids. Zbl 1109.76007
Bildhauer, M.; Fuchs, M.; Repin, S.
2007
A global nonlinear evolution problem for generalized Newtonian fluids: Local initial regularity of the strong solution. Zbl 1122.76008
Fuchs, M.; Seregin, G.
2007
Variational integrals with a wide range of anisotropy. Zbl 1284.49049
Bildhauer, M.; Fuchs, M.; Zhong, X.
2007
Continuity properties of the stress tensor in the 3-dimensional Ramberg/Osgood model. Zbl 1134.74008
Bildhauer, Michael; Fuchs, Martin
2007
On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids. Zbl 1129.35061
Bildhauer, M.; Fuchs, M.; Zhong, X.
2007
On the regularity of local minimizers of decomposable variational integrals on domains in $$\mathbb R^2$$. Zbl 1199.49075
Bildhauer, M.; Fuchs, M.
2007
Partial regularity for higher order variational problems under anisotropic growth conditions. Zbl 1149.49031
Apushkinskaya, Darya; Fuchs, Martin
2007
A functional type a posteriori error analysis for the Ramberg-Osgood model. Zbl 1128.74006
Bildhauer, Michael; Fuchs, Martin; Repin, Sergey
2007
A short remark on energy functionals related to nonlinear Hencky materials. Zbl 1154.74005
Bildhauer, Michael; Fuchs, Martin
2007
Smoothness of weak solutions of the Ramberg/Osgood equations on plane domains. Zbl 1104.74030
Bildhauer, M.; Fuchs, M.
2007
A posteriori error estimates of functional type for variational problems related to generalized Newtonian fluids. Zbl 1105.76049
Fuchs, M.; Repin, S.
2006
Higher order variational problems on two-dimensional domains. Zbl 1136.49027
Bildhauer, Michael; Fuchs, Martin
2006
$$C^{1,\alpha}$$-solutions to non-autonomous anisotropic variational problems. Zbl 1101.49029
Bildhauer, Michael; Fuchs, Martin
2005
Steady states of anisotropic generalized Newtonian fluids. Zbl 1162.76375
Apushkinskaya, Darya; Bildhauer, Michael; Fuchs, Martin
2005
A lemma on the higher integrability of functions with applications to the regularity theory of two-dimensional generalized Newtonian fluids. Zbl 1116.49018
Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao
2005
Regularization of convex variational problems with applications to generalized Newtonian fluids. Zbl 1078.76005
Bildhauer, Michael; Fuchs, Martin
2005
A regularity result for stationary electrorheological fluids in two dimensions. Zbl 1058.76073
Bildhauer, Michael; Fuchs, Martin
2004
Variants of the Stokes problem: the case of anisotropic potentials. Zbl 1072.76019
Bildhauer, Michael; Fuchs, Martin
2003
Relaxation of convex variational problems with linear growth defined on classes of vector-valued functions. Zbl 1029.49013
Bildhauer, M.; Fuchs, M.
2003
Twodimensional anisotropic variational problems. Zbl 1026.49027
Bildhauer, M.; Fuchs, M.
2003
Convex variational problems with linear growth. Zbl 1046.35020
Bildhauer, Michael; Fuchs, Martin
2003
On a class of variational integrals with linear growth satisfying the condition of $$\mu$$-ellipticity. Zbl 1047.49029
Bildhauer, Michael; Fuchs, Martin
2002
Partial regularity for a class of anisotropic variational integrals with convex hull property. Zbl 1076.49018
Bildhauer, M.; Fuchs, M.
2002
Elliptic variational problems with nonstandard growth. Zbl 1054.49026
Bildhauer, Michael; Fuchs, Martin
2002
The effect of a surface energy term on the distribution of phases in an elastic medium with a two-well elastic potential. Zbl 1131.74326
Bildhauer, Michael; Fuchs, Martin; Osmolovskiĭ, Victor
2002
Interior regularity for free and constrained local minimizers of variational integrals under general growth and ellipticity conditions. Zbl 1073.49029
Bildhauer, M.; Fuchs, M.
2002
The effect of a penalty term involving higher order derivatives on the distribution of phases in an elastic medium with a two-well elastic potential. Zbl 1032.49018
Bildhauer, M.; Fuchs, M.; Osmolovskii, V. G.
2002
Partial regularity for variational integrals with $$(s,\mu,q)$$-growth. Zbl 1018.49026
Bildhauer, Michael; Fuchs, Martin
2001
A priori gradient bounds and local $$C^{1,\alpha}$$-estimates for (double) obstacle problems under non-standard growth conditions. Zbl 1011.49024
Bildhauer, M.; Fuchs, M.; Mingione, G.
2001
Higher order variational inequalities with non-standard growth conditions in dimension two: plates with obstacles. Zbl 1014.49031
Bildhauer, Michael; Fuchs, Martin
2001
Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body. Zbl 0984.49021
Bildhauer, Michael; Fuchs, Martin; Seregin, Gregory
2001
Obstacle problems with linear growth: Hölder regularity for the dual solutions. Zbl 0995.49024
Bildhauer, Michael; Fuchs, Martin
2001
Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Zbl 0964.76003
Fuchs, Martin; Seregin, Gregory
2000
Full $$C^{1,\alpha}$$-regularity for free and constrained local minimizers of elliptic variational integrals with nearly linear growth. Zbl 0995.49023
Fuchs, Martin; Mingione, Giuseppe
2000
A two-dimensional variational model for the equilibrium configuration of an incompressible, elastic body with a three-well elastic potential. Zbl 1032.74028
Fuchs, Martin; Seregin, Gregory
2000
Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening. Zbl 0928.76087
Fuchs, Martin; Seregin, Gregory
1999
Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth. Zbl 0977.49025
Bildhauer, M.; Fuchs, M.
1999
Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Zbl 0998.81551
Fuchs, Martin; Scheffler, Matthias
1999
Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Zbl 0943.74076
Fuchs, Martin; Seregin, Gregory
1999
$$L^\infty$$-bounds for elliptic equations on Orlicz-Sobolev spaces. Zbl 0933.35053
Fuchs, Martin; Li, Gongbao
1999
A regularity theory for variational integrals with $$L\ln L$$-growth. Zbl 0929.49022
Fuchs, Martin; Seregin, Gregory
1998
Variational integrals on Orlicz-Sobolev spaces. Zbl 0913.49023
Fuchs, M.; Osmolovski, V.
1998
Variational inequalities for energy functionals with nonstandard growth conditions. Zbl 0987.49019
Fuchs, Martin; Li, Gongbao
1998
Regularity results for the quasi-static Bingham variational inequality in dimensions two and three. Zbl 0899.76044
Fuchs, Martin; Seregin, Gregory
1998
Second order obstacle problems for vectorial functions and integrands with subquadratic growth. Zbl 0910.49002
Fuchs, M.; Li, Gongbao; Martio, O.
1998
Some remarks on non-Newtonian fluids including nonconvex perturbations of the Bingham and Powell-Eyring model for viscoplastic fluids. Zbl 0882.76007
Fuchs, Martin; Seregin, Gregory
1997
Hölder continuity for weak extremals of some two-dimensional variational problems related to nonlinear elasticity. Zbl 0929.49021
Fuchs, Martin; Seregin, Gregori
1997
Global gradient bounds for relaxed variational problems. Zbl 0892.49027
Fuchs, Martin; Li, Gongbao
1997
A modification of the blowup technique for variational integrals with subquadratic growth. Zbl 0943.49030
Fuchs, Martin; Reuling, Jürgen
1997
Differentiability properties of minima of nonsmooth variational integrals. Zbl 0946.49031
Fuchs, Martin
1997
...and 47 more Documents
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### Cited by 478 Authors

 85 Fuchs, Martin 36 Bildhauer, Michael 25 Mingione, Giuseppe 20 Breit, Dominic 19 Repin, Sergeĭ Igorevich 18 Diening, Lars 17 Leonetti, Francesco 15 Duzaar, Frank 12 Passarelli di Napoli, Antonia 12 Verde, Anna 11 Bulíček, Miroslav 9 Cianchi, Andrea 9 Gmeineder, Franz 9 Málek, Josef 9 Müller, Jan-Steffen 8 De Filippis, Cristiana 8 Papageorgiou, Nikolaos S. 8 Růžička, Michael 8 Schwarzacher, Sebastian 8 Stroffolini, Bianca 7 Beck, Lisa 7 Carozza, Menita 7 Marcellini, Paolo 7 Mascolo, Elvira 7 Misawa, Masashi 7 Neff, Patrizio 7 Zhong, Xiao 6 Arkhipova, Arina A. Arkhipova 6 Frehse, Jens 6 Gao, Hongya 6 Kim, Seick 6 Kristensen, Jan 6 Rhoudaf, Mohamed 6 Schmidt, Thomas 6 Sin, Cholmin 5 Colombo, Maria 5 Cupini, Giovanni 5 Eleuteri, Michela 5 Granucci, Tiziano 5 Leone, Chiara 5 Moussa, Hassan 5 Petricca, Pier Vincenzo 5 Pigola, Stefano 5 Tietz, Christian 5 Wang, Wendong 5 Zhou, Shulin 4 Berselli, Luigi Carlo 4 Burczak, Jan 4 Byun, Sun-Sig 4 Crispo, Francesca 4 De los Reyes, Juan Carlos 4 Dolzmann, Georg 4 Fardoun, Ali 4 Focardi, Matteo 4 Giova, Raffaella 4 Kang, Kyungkeun 4 Kaplický, Petr 4 Nguyễn Thạc Dũng 4 Pauly, Dirk 4 Steffen, Klaus 4 Terasawa, Yutaka 4 Valdman, Jan 4 Veronelli, Giona 4 Zhang, Guo 4 Zhang, Kewei 3 Andersson, John Erik 3 Azroul, Elhoussine 3 Bae, Hyeong-Ohk 3 Balaadich, Farah 3 Beirão da Veiga, Hugo 3 Benseridi, Hamid 3 Caselli, Michele 3 Cho, Yumi 3 Consiglieri, Luisa 3 De Maria, Bruno 3 Dong, Hongjie 3 Esposito, Luca 3 Foss, Mikil D. 3 Gentile, Andrea 3 Huang, Miaomiao 3 Jin, Bumja 3 Kreuzer, Christian 3 Li, Shuai 3 Maz’ya, Vladimir Gilelevich 3 Nakauchi, Nobumitsu 3 Ok, Jihoon 3 Rindler, Filip 3 Schikorra, Armin 3 Seregin, Gregory A. 3 Staicu, Vasile 3 Strzelecki, Paweł 3 Süli, Endre E. 3 Weickert, Joachim 3 Ye, Yuquan 3 Zhang, Chao 3 Zhao, Peihao 3 Zheng, Jun 2 Abels, Helmut 2 Acerbi, Emilio 2 Antontsev, Stanislav Nikolaevich ...and 378 more Authors
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### Cited in 141 Serials

 42 Journal of Mathematical Sciences (New York) 39 Calculus of Variations and Partial Differential Equations 35 Manuscripta Mathematica 30 Journal of Mathematical Analysis and Applications 29 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Annali di Matematica Pura ed Applicata. Serie Quarta 17 Archive for Rational Mechanics and Analysis 17 Journal of Differential Equations 12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Journal of Mathematical Fluid Mechanics 11 St. Petersburg Mathematical Journal 9 Mathematical Methods in the Applied Sciences 8 Journal of Functional Analysis 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Nonlinear Analysis. Real World Applications 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 NoDEA. Nonlinear Differential Equations and Applications 6 Zeitschrift für Analysis und ihre Anwendungen 6 Forum Mathematicum 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Applicable Analysis 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 5 The Journal of Geometric Analysis 5 Communications in Partial Differential Equations 5 Advances in Nonlinear Analysis 4 Advances in Mathematics 4 Archiv der Mathematik 4 Geometriae Dedicata 4 Ricerche di Matematica 4 Transactions of the American Mathematical Society 4 Potential Analysis 4 Complex Variables and Elliptic Equations 4 Advances in Calculus of Variations 4 Nonlinear Analysis. Theory, Methods & Applications 3 Computers & Mathematics with Applications 3 Rocky Mountain Journal of Mathematics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Journal of the Korean Mathematical Society 3 Mathematische Nachrichten 3 Mathematische Zeitschrift 3 Numerische Mathematik 3 Revista Matemática Iberoamericana 3 SIAM Journal on Mathematical Analysis 3 Communications in Contemporary Mathematics 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Communications on Pure and Applied Analysis 3 Boundary Value Problems 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Afrika Matematika 3 Journal of Elliptic and Parabolic Equations 2 Journal of Mathematical Physics 2 Applied Mathematics and Computation 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Inventiones Mathematicae 2 Journal of Optimization Theory and Applications 2 Kybernetika 2 Mathematische Annalen 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Rendiconti del Seminario Matematico della Università di Padova 2 SIAM Journal on Control and Optimization 2 SIAM Journal on Numerical Analysis 2 Journal of Scientific Computing 2 International Journal of Mathematics 2 Applications of Mathematics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Electronic Journal of Differential Equations (EJDE) 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Journal of Applied Analysis 2 Abstract and Applied Analysis 2 Positivity 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Journal of the European Mathematical Society (JEMS) 2 Computational Methods in Applied Mathematics 2 Mediterranean Journal of Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Inverse Problems 1 Nonlinearity 1 Ukrainian Mathematical Journal 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Arkiv för Matematik 1 Annales Polonici Mathematici 1 Applied Mathematics and Optimization 1 Journal of Computational and Applied Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Soviet Mathematics 1 Mathematics and Computers in Simulation 1 Monatshefte für Mathematik 1 Tôhoku Mathematical Journal. Second Series 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Bulletin of the Korean Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Journal of Integral Equations and Applications 1 Science in China. Series A 1 Differential Geometry and its Applications 1 International Journal of Computer Mathematics ...and 41 more Serials
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### Cited in 31 Fields

 394 Partial differential equations (35-XX) 213 Calculus of variations and optimal control; optimization (49-XX) 97 Fluid mechanics (76-XX) 67 Global analysis, analysis on manifolds (58-XX) 46 Mechanics of deformable solids (74-XX) 36 Differential geometry (53-XX) 35 Functional analysis (46-XX) 31 Numerical analysis (65-XX) 25 Real functions (26-XX) 14 Operator theory (47-XX) 13 Potential theory (31-XX) 13 Information and communication theory, circuits (94-XX) 7 Functions of a complex variable (30-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Computer science (68-XX) 5 Ordinary differential equations (34-XX) 5 Optics, electromagnetic theory (78-XX) 3 History and biography (01-XX) 3 Probability theory and stochastic processes (60-XX) 3 Operations research, mathematical programming (90-XX) 2 Measure and integration (28-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Relativity and gravitational theory (83-XX) 2 Geophysics (86-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX)