# zbMATH — the first resource for mathematics

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 Documents Indexed: 51 Publications since 1972, including 2 Books
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#### Co-Authors

 23 single-authored 7 Sohr, Hermann 5 Louhivaara, Ilppo Simo 4 Galdi, Giovanni Paolo 3 Leinfelder, Herbert 3 Russo, Remigio 2 Drábek, Pavel 2 Farwig, Reinhard 2 Varnhorn, Werner 1 Kufner, Alois 1 Mustonen, Vesa 1 Naumann, Joachim 1 von Wahl, Wolf 1 Weyers, Stephan 1 Ziegler, Thomas R.
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#### Serials

 5 Mathematische Zeitschrift 4 Analysis (München) 3 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Mathematica Bohemica 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Mathematical Methods in the Applied Sciences 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal für die Reine und Angewandte Mathematik 1 Le Matematiche 1 Mathematische Annalen 1 Results in Mathematics 1 Ricerche di Matematica 1 Zeitschrift für Analysis und ihre Anwendungen 1 Differential and Integral Equations 1 Expositiones Mathematicae 1 Bayreuther Mathematische Schriften 1 Journal of Mathematical Fluid Mechanics 1 Lecture Notes in Mathematics 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Annales Academiae Scientiarum Fennicae. Series A I
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#### Fields

 47 Partial differential equations (35-XX) 11 Fluid mechanics (76-XX) 9 Functional analysis (46-XX) 8 Operator theory (47-XX) 3 Potential theory (31-XX) 3 Mechanics of deformable solids (74-XX) 2 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX)

#### Citations contained in zbMATH

41 Publications have been cited 591 times in 502 Documents Cited by Year
Schrödinger operators with singular magnetic vector potentials. Zbl 0468.35038
1981
A new approach to the Helmholtz decomposition and the Neumann problem in $$L^ q$$-spaces for bounded and exterior domains. Zbl 0791.35096
1992
On Dirichlet’s boundary value problem. An $$L^p$$-theory based on a generalization of Garding’s inequality. Zbl 0242.35027
1972
Existence, uniqueness and $$L^ q$$-estimates for the Stokes problem in an exterior domain. Zbl 0722.35065
Galdi, Giovanni P.; Simader, Christian G.
1990
The Dirichlet problem for the Laplacian in bounded and unbounded domains. Zbl 0868.35001
1996
A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in $$W^{-1/q,q}$$. Zbl 1064.35133
Galdi, G. P.; Simader, C. G.; Sohr, H.
2005
On the Stokes problem in Lipschitz domains. Zbl 0824.35098
Galdi, G. P.; Simader, C. G.; Sohr, H.
1994
An elementary proof of Harnack’s inequality for Schrödinger operators and related topics. Zbl 0697.35017
1990
Essential self-adjointness of Schrödinger operators bounded from below. Zbl 0409.35026
1978
Bemerkungen über Schrödinger-Operatoren mit stark singulären Potentialen. Zbl 0317.35028
1974
Über schwache Lösungen des Dirichletproblems für streng nichtlineare elliptische Differentialgleichungen. Zbl 0354.35039
1976
New estimates for the steady-state Stokes problem in exterior domains with applications to the Navier-Stokes problem. Zbl 0823.35142
Galdi, Giovanni P.; Simader, Christian G.
1994
The weak Dirichlet and Neumann problem for the Laplacian in $$L^ q$$ for bounded and exterior domains. Applications. Zbl 0786.35036
1990
Mean value formulas, Weyl’s lemma and Liouville theorems for $$\Delta^ 2$$ and Stokes’ system. Zbl 0766.31006
1992
A note on the existence of solutions to the Oseen system in Lipschitz domains. Zbl 1099.76017
2006
Equivalence of weak Dirichlet’s principle, the method of weak solutions and Perron’s method towards classical solutions of Dirichlet’s problem for harmonic functions. Zbl 1163.35003
2006
Nonlinear eigenvalue problems for quasilinear equations in unbounded domains. Zbl 0936.35066
1999
Remarks on uniqueness and stability of weak solutions of strongly nonlinear elliptic equations. Zbl 0501.35034
1982
An $$L^ q$$-theory for weak solutions of the Stokes system in exterior domains. Zbl 0787.35063
Farwig, R.; Simader, C. G.; Sohr, H.
1993
On the existence and uniqueness of solutions for strongly nonlinear elliptic variational problems. Zbl 0513.35033
1981
Another approach to the Dirichlet problem for very strongly nonlinear elliptic equations. Zbl 0348.35037
1976
Bemerkungen über nichtlineare Störungen von Schrödinger-Operatoren. Zbl 0323.35031
1975
General properties of the Helmholtz decomposition in spaces of $$L^q$$-type. Zbl 1349.35292
Farwig, Reinhard; Simader, Christian; Sohr, Hermann; Varnhorn, Werner
2016
Necessary and sufficient conditions for the existence of Helmholtz decompositions in general domains. Zbl 1304.35506
Simader, Christian G.; Sohr, Hermann; Varnhorn, Werner
2014
On the exterior two-dimensional Dirichlet problem for elliptic equations. Zbl 1192.35041
2009
An operator related to the Cosserat spectrum. Applications. Zbl 1157.35034
2006
The weak $$L^q$$-Cosserat spectrum for the first boundary value problem in the half-space. Applications to Stokes’ and Lamé’s system. Zbl 1157.35033
2006
Introduction to the Cosserat problem. Zbl 1157.35035
Simader, Christian G.; von Wahl, Wolf
2006
The Helmholtz decomposition and the weak Neumann problem in $$L^ q$$. Zbl 0723.35024
1990
Sketch of an alternative approach to weak $$L^q$$-solutions of Stokes’ system in a half-space. Zbl 1330.35346
2002
On general solvability properties of $$p$$-Laplacian-like equations. Zbl 1030.35058
2002
A second look on definition and equivalent norms of Sobolev spaces. Zbl 0941.46019
1999
Sobolev’s original definition of his spaces revisited and a comparison with nowadays definition. Zbl 0947.46022
1999
The weak Dirichlet and Neumann problems in $$L^q$$ for the Laplacian and the Helmholtz decomposition in infinite cylinders and layers. Zbl 0932.35058
1998
Hardy inequalities for overdetermined classes of functions. Zbl 0895.26003
1997
Remarks on essential self-adjointness of Schrödinger operators with singular electrostatic potentials. Zbl 0776.35009
1992
The Brouwer fixed point theorem and the transformation rule for multiple integrals via homotopy arguments. Zbl 0534.47038
1983
Über periodische Lösungen koerzitiver linearer partieller Differentialgleichungen. Zbl 0426.35027
Louhivaara, Ilppo Simo; Simader, Christian G.
1979
Über koerzitive lineare partielle Differentialoperatoren: Fredholmsche verallgemeinerte Dirichletprobleme und deren Klasseneinteilung. Zbl 0431.35019
Louhivaara, Ilppo Simo; Simader, Christian G.
1978
Über das verallgemeinerte Dirichletproblem für koerzitive lineare partielle Differentialgleichungen. Zbl 0355.35016
Louhivaara, Ilppo Simo; Simader, Christian G.
1976
Über nichtelliptische lineare partielle Differentialoperatoren mit konstanten Koeffizienten. Zbl 0251.35073
Louhivaara, Ilppo Simo; Simader, Christian G.
1972
General properties of the Helmholtz decomposition in spaces of $$L^q$$-type. Zbl 1349.35292
Farwig, Reinhard; Simader, Christian; Sohr, Hermann; Varnhorn, Werner
2016
Necessary and sufficient conditions for the existence of Helmholtz decompositions in general domains. Zbl 1304.35506
Simader, Christian G.; Sohr, Hermann; Varnhorn, Werner
2014
On the exterior two-dimensional Dirichlet problem for elliptic equations. Zbl 1192.35041
2009
A note on the existence of solutions to the Oseen system in Lipschitz domains. Zbl 1099.76017
2006
Equivalence of weak Dirichlet’s principle, the method of weak solutions and Perron’s method towards classical solutions of Dirichlet’s problem for harmonic functions. Zbl 1163.35003
2006
An operator related to the Cosserat spectrum. Applications. Zbl 1157.35034
2006
The weak $$L^q$$-Cosserat spectrum for the first boundary value problem in the half-space. Applications to Stokes’ and Lamé’s system. Zbl 1157.35033
2006
Introduction to the Cosserat problem. Zbl 1157.35035
Simader, Christian G.; von Wahl, Wolf
2006
A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in $$W^{-1/q,q}$$. Zbl 1064.35133
Galdi, G. P.; Simader, C. G.; Sohr, H.
2005
Sketch of an alternative approach to weak $$L^q$$-solutions of Stokes’ system in a half-space. Zbl 1330.35346
2002
On general solvability properties of $$p$$-Laplacian-like equations. Zbl 1030.35058
2002
Nonlinear eigenvalue problems for quasilinear equations in unbounded domains. Zbl 0936.35066
1999
A second look on definition and equivalent norms of Sobolev spaces. Zbl 0941.46019
1999
Sobolev’s original definition of his spaces revisited and a comparison with nowadays definition. Zbl 0947.46022
1999
The weak Dirichlet and Neumann problems in $$L^q$$ for the Laplacian and the Helmholtz decomposition in infinite cylinders and layers. Zbl 0932.35058
1998
Hardy inequalities for overdetermined classes of functions. Zbl 0895.26003
1997
The Dirichlet problem for the Laplacian in bounded and unbounded domains. Zbl 0868.35001
1996
On the Stokes problem in Lipschitz domains. Zbl 0824.35098
Galdi, G. P.; Simader, C. G.; Sohr, H.
1994
New estimates for the steady-state Stokes problem in exterior domains with applications to the Navier-Stokes problem. Zbl 0823.35142
Galdi, Giovanni P.; Simader, Christian G.
1994
An $$L^ q$$-theory for weak solutions of the Stokes system in exterior domains. Zbl 0787.35063
Farwig, R.; Simader, C. G.; Sohr, H.
1993
A new approach to the Helmholtz decomposition and the Neumann problem in $$L^ q$$-spaces for bounded and exterior domains. Zbl 0791.35096
1992
Mean value formulas, Weyl’s lemma and Liouville theorems for $$\Delta^ 2$$ and Stokes’ system. Zbl 0766.31006
1992
Remarks on essential self-adjointness of Schrödinger operators with singular electrostatic potentials. Zbl 0776.35009
1992
Existence, uniqueness and $$L^ q$$-estimates for the Stokes problem in an exterior domain. Zbl 0722.35065
Galdi, Giovanni P.; Simader, Christian G.
1990
An elementary proof of Harnack’s inequality for Schrödinger operators and related topics. Zbl 0697.35017
1990
The weak Dirichlet and Neumann problem for the Laplacian in $$L^ q$$ for bounded and exterior domains. Applications. Zbl 0786.35036
1990
The Helmholtz decomposition and the weak Neumann problem in $$L^ q$$. Zbl 0723.35024
1990
The Brouwer fixed point theorem and the transformation rule for multiple integrals via homotopy arguments. Zbl 0534.47038
1983
Remarks on uniqueness and stability of weak solutions of strongly nonlinear elliptic equations. Zbl 0501.35034
1982
Schrödinger operators with singular magnetic vector potentials. Zbl 0468.35038
1981
On the existence and uniqueness of solutions for strongly nonlinear elliptic variational problems. Zbl 0513.35033
1981
Über periodische Lösungen koerzitiver linearer partieller Differentialgleichungen. Zbl 0426.35027
Louhivaara, Ilppo Simo; Simader, Christian G.
1979
Essential self-adjointness of Schrödinger operators bounded from below. Zbl 0409.35026
1978
Über koerzitive lineare partielle Differentialoperatoren: Fredholmsche verallgemeinerte Dirichletprobleme und deren Klasseneinteilung. Zbl 0431.35019
Louhivaara, Ilppo Simo; Simader, Christian G.
1978
Über schwache Lösungen des Dirichletproblems für streng nichtlineare elliptische Differentialgleichungen. Zbl 0354.35039
1976
Another approach to the Dirichlet problem for very strongly nonlinear elliptic equations. Zbl 0348.35037
1976
Über das verallgemeinerte Dirichletproblem für koerzitive lineare partielle Differentialgleichungen. Zbl 0355.35016
Louhivaara, Ilppo Simo; Simader, Christian G.
1976
Bemerkungen über nichtlineare Störungen von Schrödinger-Operatoren. Zbl 0323.35031
1975
Bemerkungen über Schrödinger-Operatoren mit stark singulären Potentialen. Zbl 0317.35028
1974
On Dirichlet’s boundary value problem. An $$L^p$$-theory based on a generalization of Garding’s inequality. Zbl 0242.35027
1972
Über nichtelliptische lineare partielle Differentialoperatoren mit konstanten Koeffizienten. Zbl 0251.35073
Louhivaara, Ilppo Simo; Simader, Christian G.
1972
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#### Cited by 502 Authors

 15 Simader, Christian Georg 14 Kozono, Hideo 13 Amrouche, Chérif 12 Farwig, Reinhard 12 Sohr, Hermann 11 Maremonti, Paolo 9 Kim, Hyunseok 9 Medková, Dagmar 8 Russo, Remigio 8 Wolf, Jörg 7 Galdi, Giovanni Paolo 7 Tartaglione, Alfonsina 6 Byun, Sun-Sig 6 Hishida, Toshiaki 6 Meslameni, Mohamed 6 Schumacher, Katrin 6 Varnhorn, Werner 5 Choe, Hi Jun 5 Giga, Yoshikazu 5 Raikov, Georgi D. 5 Rakotoson, Jean-Michel 5 Shen, Zhongwei 5 Taniuchi, Yasushi 4 Abe, Ken 4 Al Baba, Hind 4 Borchers, Wolfgang 4 Deuring, Paul 4 Han, Qi 4 Landes, Rüdiger 4 Leinfelder, Herbert 4 Maz’ya, Vladimir Gilelevich 4 Rodríguez-Bellido, Maria Angeles 4 Růžička, Michael 4 Semenov, Yuriy A. 4 Shubin, Mikhail Aleksandrovich 4 Simon, Barry 4 Tehrani, Hossein Torabi 4 Yanagisawa, Taku 4 Zamboni, Pietro 3 Abels, Helmut 3 Amann, Herbert 3 Auchmuty, Giles 3 Bidaut-Veron, Marie-Françoise 3 Bui, The Anh 3 Carl, Siegfried 3 Chae, Dongho 3 Chueshov, Igor’ Dmitrievich 3 Costa, David Goldstein 3 Di Fazio, Giuseppe 3 Enstedt, Mattias 3 Fanelli, Luca 3 Frehse, Jens 3 Hieber, Matthias 3 Hinz, Andreas M. 3 Ichinose, Takashi 3 Iftimie, Viorel 3 Kalf, Hubert 3 Kondrat’ev, Vladimir Aleksandrovich 3 Liskevich, Vitaliĭ A. 3 Maekawa, Yasunori 3 Melgaard, Michael 3 Milatovic, Ognjen 3 Mitrea, Marius 3 Miyakawa, Tetsuro 3 Nakao, Kohei 3 Nakatsuka, Tomoyuki 3 Nečasová, Šárka 3 Pan, Xingbin 3 Pileckas, Konstantin 3 Riechwald, Paul Felix 3 Russo, Antonio 3 Saal, Jürgen 3 Shibata, Yoshihiro 3 Vega, Luis 3 Voigt, Jurgen 3 Wang, Lihe 3 Yamazaki, Masao 2 Abe, Kenichi 2 Agouzal, Abdellatif 2 Aliev, Araz R. 2 Allali, Karam 2 Alliot, Frédéric 2 Bae, Hyeong-Ohk 2 Beirão da Veiga, Hugo 2 Benjemaa, Mondher 2 Berselli, Luigi Carlo 2 Binna, Siham 2 Black, Tobias 2 Boulmezaoud, Tahar Zamène 2 Clément, Philippe J. E. 2 Coscia, Vincenzo 2 D’Ancona, Piero 2 Diaz Diaz, Jesus Ildefonso 2 Duong, Xuan Thinh 2 El Berdan, Nada Kassem 2 Fastovska, Tamara 2 Ferone, Adele 2 Gao, Huadong 2 Germinet, François 2 Gesztesy, Fritz ...and 402 more Authors
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#### Cited in 136 Serials

 32 Journal of Differential Equations 22 Journal of Functional Analysis 22 Mathematische Zeitschrift 21 Archive for Rational Mechanics and Analysis 21 Journal of Mathematical Analysis and Applications 17 Mathematische Annalen 16 Journal of Mathematical Fluid Mechanics 12 Manuscripta Mathematica 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Communications in Partial Differential Equations 10 Journal of Mathematical Physics 8 Communications in Mathematical Physics 8 Mathematical Methods in the Applied Sciences 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Mathematische Nachrichten 8 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 7 Czechoslovak Mathematical Journal 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Calculus of Variations and Partial Differential Equations 6 Advances in Mathematics 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 SIAM Journal on Mathematical Analysis 6 Journal of Evolution Equations 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 Transactions of the American Mathematical Society 5 Acta Applicandae Mathematicae 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Discrete and Continuous Dynamical Systems 4 Mathematics of Computation 4 Reviews in Mathematical Physics 4 Integral Equations and Operator Theory 4 Journal of the Mathematical Society of Japan 4 Numerische Mathematik 4 Proceedings of the American Mathematical Society 4 Analysis (München) 4 Annales Henri Poincaré 3 Applicable Analysis 3 Journal d’Analyse Mathématique 3 Letters in Mathematical Physics 3 Lithuanian Mathematical Journal 3 Ukrainian Mathematical Journal 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Acta Mathematica 3 Rendiconti del Seminario Matematico della Università di Padova 3 Tohoku Mathematical Journal. Second Series 3 Acta Mathematica Hungarica 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Potential Analysis 3 Journal of Mathematical Sciences (New York) 3 Discrete and Continuous Dynamical Systems. Series B 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Mediterranean Journal of Mathematics 3 Journal of Pseudo-Differential Operators and Applications 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applied Mathematics and Optimization 2 Duke Mathematical Journal 2 Functional Analysis and its Applications 2 Journal of Computational and Applied Mathematics 2 Journal of Optimization Theory and Applications 2 Monatshefte für Mathematik 2 Numerical Functional Analysis and Optimization 2 Results in Mathematics 2 Numerical Methods for Partial Differential Equations 2 Applied Mathematics Letters 2 The Journal of Geometric Analysis 2 NoDEA. Nonlinear Differential Equations and Applications 2 Abstract and Applied Analysis 2 Mathematical Physics, Analysis and Geometry 2 Nonlinear Analysis. Real World Applications 2 Communications on Pure and Applied Analysis 2 Differential Equations and Applications 2 Bulletin of Mathematical Sciences 2 Advances in Nonlinear Analysis 2 Journal of Elliptic and Parabolic Equations 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 International Journal of Theoretical Physics 1 Journal of Statistical Physics 1 Mathematical Notes 1 Reports on Mathematical Physics 1 Arkiv för Matematik 1 Journal of Geometry and Physics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Applied Mathematics and Computation 1 Archiv der Mathematik 1 Boletim da Sociedade Brasileira de Matemática 1 Hiroshima Mathematical Journal 1 Inventiones Mathematicae 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Ricerche di Matematica 1 SIAM Journal on Numerical Analysis 1 Siberian Mathematical Journal 1 Tokyo Journal of Mathematics ...and 36 more Serials
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#### Cited in 38 Fields

 440 Partial differential equations (35-XX) 186 Fluid mechanics (76-XX) 101 Operator theory (47-XX) 65 Quantum theory (81-XX) 42 Functional analysis (46-XX) 27 Numerical analysis (65-XX) 24 Global analysis, analysis on manifolds (58-XX) 14 Potential theory (31-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 12 Mechanics of deformable solids (74-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Probability theory and stochastic processes (60-XX) 8 Optics, electromagnetic theory (78-XX) 7 Ordinary differential equations (34-XX) 7 Biology and other natural sciences (92-XX) 6 Real functions (26-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Differential geometry (53-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Measure and integration (28-XX) 4 Integral equations (45-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)