Bildhauer, Michael; Farquhar, Bernhard; Fuchs, Martin A small remark on Bernstein’s theorem. (English) Zbl 07742428 Arch. Math. 121, No. 4, 437-447 (2023). Reviewer: Georgios Psaradakis (Kastoria) MSC: 49Q20 49Q05 53A10 35J20 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., Arch. Math. 121, No. 4, 437--447 (2023; Zbl 07742428) Full Text: DOI arXiv OA License
Bildhauer, Michael; Fuchs, Martin On the global regularity for minimizers of variational integrals: splitting-type problems in 2D and extensions to the general anisotropic setting. (English) Zbl 1500.49021 J. Elliptic Parabol. Equ. 8, No. 2, 853-884 (2022). MSC: 49N60 49Q20 49J45 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Elliptic Parabol. Equ. 8, No. 2, 853--884 (2022; Zbl 1500.49021) Full Text: DOI arXiv
Bildhauer, Michael; Fuchs, Martin Splitting-type variational problems with mixed linear-superlinear growth conditions. (English) Zbl 1466.49009 J. Math. Anal. Appl. 501, No. 1, Article ID 124452, 29 p. (2021). MSC: 49J45 49Q20 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Math. Anal. Appl. 501, No. 1, Article ID 124452, 29 p. (2021; Zbl 1466.49009) Full Text: DOI
Bildhauer, M.; Fuchs, M. Splitting type variational problems with linear growth conditions. (English. Russian original) Zbl 1448.49011 J. Math. Sci., New York 250, No. 2, 232-249 (2020); translation from Probl. Mat. Anal. 105, 45-58 (2020). MSC: 49J30 35B65 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Math. Sci., New York 250, No. 2, 232--249 (2020; Zbl 1448.49011); translation from Probl. Mat. Anal. 105, 45--58 (2020) Full Text: DOI arXiv
Fuchs, M.; Weickert, J. Iterative TV-regularization of grey-scale images. (English. Russian original) Zbl 1427.94013 J. Math. Sci., New York 242, No. 2, 323-336 (2019); translation from Probl. Mat. Anal. 99, 127-137 (2019). MSC: 94A08 68U10 49N60 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{J. Weickert}, J. Math. Sci., New York 242, No. 2, 323--336 (2019; Zbl 1427.94013); translation from Probl. Mat. Anal. 99, 127--137 (2019) Full Text: DOI
Bildhauer, M.; Fuchs, M.; Müller, J. Existence and regularity for stationary incompressible flows with dissipative potentials of linear growth. (English) Zbl 1404.76011 J. Math. Fluid Mech. 20, No. 4, 1567-1587 (2018). MSC: 76A05 76M30 49Q20 49N60 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Math. Fluid Mech. 20, No. 4, 1567--1587 (2018; Zbl 1404.76011) Full Text: DOI
Bildhauer, M.; Fuchs, M.; Müller, J.; Zhong, X. On the local boundedness of generalized minimizers of variational problems with linear growth. (English) Zbl 1401.49066 Ann. Mat. Pura Appl. (4) 197, No. 4, 1117-1129 (2018). Reviewer: Stepan Agop Tersian (Rousse) MSC: 49Q20 49J45 49N60 94A08 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., Ann. Mat. Pura Appl. (4) 197, No. 4, 1117--1129 (2018; Zbl 1401.49066) Full Text: DOI arXiv
Fuchs, M.; Müller, J.; Tietz, C. Signal recovery via TV-type energies. (English) Zbl 1392.49003 St. Petersbg. Math. J. 29, No. 4, 657-681 (2018) and Algebra Anal. 29, No. 4, 159-195 (2017). MSC: 49J05 49N60 26A45 49J45 34B15 PDFBibTeX XMLCite \textit{M. Fuchs} et al., St. Petersbg. Math. J. 29, No. 4, 657--681 (2018; Zbl 1392.49003) Full Text: DOI arXiv
Fuchs, Martin; Müller, Jan; Tietz, Christian; Weickert, Joachim Convex regularization of multi-channel images based on variants of the TV-model. (English) Zbl 1391.49020 Complex Var. Elliptic Equ. 63, No. 7-8, 976-995 (2018). MSC: 49J45 49Q20 49N60 PDFBibTeX XMLCite \textit{M. Fuchs} et al., Complex Var. Elliptic Equ. 63, No. 7--8, 976--995 (2018; Zbl 1391.49020) Full Text: DOI arXiv
Fuchs, M.; Müller, J. A remark on denoising of greyscale images using energy densities with varying growth rates. (English. Russian original) Zbl 1398.49032 J. Math. Sci., New York 228, No. 6, 705-722 (2018); translation from Probl. Mat. Anal. 90, 91-105 (2018). Reviewer: Vasile Lupulescu (Târgu Jiu) MSC: 49N60 49K27 49J27 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{J. Müller}, J. Math. Sci., New York 228, No. 6, 705--722 (2018; Zbl 1398.49032); translation from Probl. Mat. Anal. 90, 91--105 (2018) Full Text: DOI arXiv
Bildhauer, M.; Fuchs, M.; Weickert, J. An alternative approach towards the higher order denoising of images. analytical aspects. (English) Zbl 1384.35019 J. Math. Sci., New York 224, No. 3, 414-441 (2017) and Zap. Nauchn. Semin. POMI 444, 47-88 (2016). Reviewer: Guy Jumarie (Montréal) MSC: 35J20 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Math. Sci., New York 224, No. 3, 414--441 (2017; Zbl 1384.35019) Full Text: DOI
Fuchs, Martin; Müller, Jan A higher order TV-type variational problem related to the denoising and inpainting of images. (English) Zbl 1358.49043 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 154, 122-147 (2017). MSC: 49Q20 49N60 49N15 94A08 62H35 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{J. Müller}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 154, 122--147 (2017; Zbl 1358.49043) Full Text: DOI arXiv
Bildhauer, M.; Fuchs, M.; Müller, J.; Tietz, C. On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case. (English) Zbl 1382.49044 J. Elliptic Parabol. Equ. 2, No. 1-2, 341-355 (2016). MSC: 49N60 62H35 49K27 94A08 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Elliptic Parabol. Equ. 2, No. 1--2, 341--355 (2016; Zbl 1382.49044) Full Text: DOI arXiv
Bildhauer, M.; Fuchs, M.; Weickert, J. Denoising and inpainting of images using TV-type energies: theoretical and computational aspects. (English. Russian original) Zbl 1381.94011 J. Math. Sci., New York 219, No. 6, 899-910 (2016); translation from Probl. Mat. Anal. 87, 69-78 (2016). MSC: 94A08 49J10 68U10 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Math. Sci., New York 219, No. 6, 899--910 (2016; Zbl 1381.94011); translation from Probl. Mat. Anal. 87, 69--78 (2016) Full Text: DOI
Bildhauer, M.; Fuchs, M.; Tietz, C. \(C^{1,\alpha}\)-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting. (English) Zbl 1335.49058 St. Petersbg. Math. J. 27, No. 3, 381-392 (2016) and Algebra Anal. 27, No. 3, 51-65 (2015). MSC: 49N60 49Q20 94A08 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., St. Petersbg. Math. J. 27, No. 3, 381--392 (2016; Zbl 1335.49058) Full Text: DOI
Fuchs, M.; Tietz, C. Existence of generalized minimizers and dual solutions for a class of variational problems with linear growth related to image recovery. (English. Russian original) Zbl 1331.49014 J. Math. Sci., New York 210, No. 4, 458-475 (2015); translation from Probl. Mat. Anal. 81, 107-120 (2015). MSC: 49J45 49N15 26B30 94A08 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{C. Tietz}, J. Math. Sci., New York 210, No. 4, 458--475 (2015; Zbl 1331.49014); translation from Probl. Mat. Anal. 81, 107--120 (2015) Full Text: DOI
Bildhauer, M.; Fuchs, M. On some perturbations of the total variation image inpainting method. III: Minimization among sets with finite perimeter. (English. Russian original) Zbl 1335.49024 J. Math. Sci., New York 207, No. 2, 142-146 (2015); translation from Probl. Mat. Anal. 78, 27-30 (2015). MSC: 49J45 94A08 68U10 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Math. Sci., New York 207, No. 2, 142--146 (2015; Zbl 1335.49024); translation from Probl. Mat. Anal. 78, 27--30 (2015) Full Text: DOI
Bildhauer, M.; Fuchs, M. On some perturbations of the total variation image inpainting method. II: Relaxation and dual variational formulation. (English. Russian original) Zbl 1321.49054 J. Math. Sci., New York 205, No. 2, 121-140 (2015); translation from Probl. Mat. Anal. 77, 3-18 (2014). MSC: 49N15 49J45 94A08 68U10 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Math. Sci., New York 205, No. 2, 121--140 (2015; Zbl 1321.49054); translation from Probl. Mat. Anal. 77, 3--18 (2014) Full Text: DOI
Bildhauer, M.; Fuchs, M. On some perturbations of the total variation image inpainting method. I: Regularity theory. (English. Russian original) Zbl 1321.49060 J. Math. Sci., New York 202, No. 2, 154-169 (2014); translation from Probl. Mat. Anal. 76, 39-52 (2014). MSC: 49N60 94A08 68U10 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Math. Sci., New York 202, No. 2, 154--169 (2014; Zbl 1321.49060); translation from Probl. Mat. Anal. 76, 39--52 (2014) Full Text: DOI
Bildhauer, M.; Fuchs, M. Image inpainting with energies of linear growth. A collection of proposals. (English. Russian original) Zbl 1302.49004 J. Math. Sci., New York 196, No. 4, 490-497 (2014); translation from Probl. Mat. Anal. 74, 45-50 (2013). MSC: 49J20 49N60 94A08 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, J. Math. Sci., New York 196, No. 4, 490--497 (2014; Zbl 1302.49004); translation from Probl. Mat. Anal. 74, 45--50 (2013) Full Text: DOI
Bildhauer, Michael; Fuchs, Martin; Zhang, Guo Liouville-type theorems for steady flows of degenerate power law fluids in the plane. (English) Zbl 1273.76076 J. Math. Fluid Mech. 15, No. 3, 583-616 (2013). MSC: 76D05 76D07 76M30 35Q30 35Q35 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., J. Math. Fluid Mech. 15, No. 3, 583--616 (2013; Zbl 1273.76076) Full Text: DOI arXiv
Bildhauer, M.; Fuchs, M. Lipschitz regularity for constrained local minimizers of convex variational integrals with a wide range of anisotropy. (English) Zbl 1263.49039 Manuscr. Math. 141, No. 1-2, 63-83 (2013). MSC: 49N60 35J86 49J40 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, Manuscr. Math. 141, No. 1--2, 63--83 (2013; Zbl 1263.49039) Full Text: DOI
Fuchs, M.; Zhang, G. On entire solutions of the equations for the displacement fields in the deformation theory of plasticity with logarithmic hardening. (English. Russian original) Zbl 1278.35243 J. Math. Sci., New York 185, No. 5, 746-753 (2012); translation from Zap. Nauchn. Semin. POMI 397, 157-171 (2011). MSC: 35Q74 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{G. Zhang}, J. Math. Sci., New York 185, No. 5, 746--753 (2012; Zbl 1278.35243); translation from Zap. Nauchn. Semin. POMI 397, 157--171 (2011) Full Text: DOI
Breit, D.; Diening, L.; Fuchs, M. Solenoidal Lipschitz truncation and applications in fluid mechanics. (English) Zbl 1245.35080 J. Differ. Equations 253, No. 6, 1910-1942 (2012). MSC: 35Q30 35J60 35Q35 76A05 76B03 PDFBibTeX XMLCite \textit{D. Breit} et al., J. Differ. Equations 253, No. 6, 1910--1942 (2012; Zbl 1245.35080) Full Text: DOI
Fuchs, Martin; Zhang, Guo 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. (English) Zbl 1252.49075 Calc. Var. Partial Differ. Equ. 44, No. 1-2, 271-295 (2012). Reviewer: Elvira Mascolo (Firenze) MSC: 49S05 49N60 35J50 35Q30 76D05 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{G. Zhang}, Calc. Var. Partial Differ. Equ. 44, No. 1--2, 271--295 (2012; Zbl 1252.49075) Full Text: DOI
Fuchs, M. Two-dimensional variational problems with a wide range of anisotropy. (English. Russian original) Zbl 1279.49026 J. Math. Sci., New York 175, No. 3, 375-389 (2011); translation from Probl. Mat. Anal. 56, 137-148 (2011). MSC: 49N60 PDFBibTeX XMLCite \textit{M. Fuchs}, J. Math. Sci., New York 175, No. 3, 375--389 (2011; Zbl 1279.49026); translation from Probl. Mat. Anal. 56, 137--148 (2011) Full Text: DOI
Fuchs, M.; Bildhauer, M. Compact embeddings of the space of functions with bounded logarithmic deformation. (English. Russian original) Zbl 1229.46023 J. Math. Sci., New York 172, No. 1, 165-183 (2011); translation from Probl. Mat. Anal. 51, 139-153 (2010). MSC: 46E35 46E30 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{M. Bildhauer}, J. Math. Sci., New York 172, No. 1, 165--183 (2011; Zbl 1229.46023); translation from Probl. Mat. Anal. 51, 139--153 (2010) Full Text: DOI
Fuchs, M.; Repin, S. A posteriori error estimates for the approximations of the stresses in the Hencky plasticity problem. (English) Zbl 1419.74076 Numer. Funct. Anal. Optim. 32, No. 6, 610-640 (2011). MSC: 74C05 74G65 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{S. Repin}, Numer. Funct. Anal. Optim. 32, No. 6, 610--640 (2011; Zbl 1419.74076) Full Text: DOI
Fuchs, Martin Local Lipschitz regularity of vector valued local minimizers of variational integrals with densities depending on the modulus of the gradient. (English) Zbl 1211.49047 Math. Nachr. 284, No. 2-3, 266-272 (2011). MSC: 49N60 35J50 PDFBibTeX XMLCite \textit{M. Fuchs}, Math. Nachr. 284, No. 2--3, 266--272 (2011; Zbl 1211.49047) Full Text: DOI
Apushkinskaya, D.; Bildhauer, M.; Fuchs, M. On local generalized minimizers and local stress tensors for variational problems with linear growth. (English. Russian original) Zbl 1301.49096 J. Math. Sci., New York 165, No. 1, 42-59 (2010); translation from Probl. Mat. Anal. 44, 39-54 (2010). MSC: 49N60 PDFBibTeX XMLCite \textit{D. Apushkinskaya} et al., J. Math. Sci., New York 165, No. 1, 42--59 (2010; Zbl 1301.49096); translation from Probl. Mat. Anal. 44, 39--54 (2010) Full Text: DOI DOI
Fuchs, M. Regularity results for local minimizers of energies with general densities having superquadratic growth. (English. Russian original) Zbl 1207.49046 St. Petersbg. Math. J. 21, No. 5, 825-838 (2010); translation from Algebra Anal. 21, No. 5, 203-221 (2009). MSC: 49N60 PDFBibTeX XMLCite \textit{M. Fuchs}, St. Petersbg. Math. J. 21, No. 5, 825--838 (2010; Zbl 1207.49046); translation from Algebra Anal. 21, No. 5, 203--221 (2009) Full Text: DOI
Fuchs, M.; Repin, S. Estimates of the deviations from the exact solutions for variational inequalities describing the stationary flow of certain viscous incompressible fluids. (English) Zbl 1357.76062 Math. Methods Appl. Sci. 33, No. 9, 1136-1147 (2010). MSC: 76M25 76D03 35Q35 65K15 76A05 49J40 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{S. Repin}, Math. Methods Appl. Sci. 33, No. 9, 1136--1147 (2010; Zbl 1357.76062) Full Text: DOI
Bildhauer, Michael; Fuchs, Martin Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials. (English) Zbl 1189.49057 Calc. Var. Partial Differ. Equ. 37, No. 1-2, 167-186 (2010). MSC: 49N60 74B20 74G40 74G65 PDFBibTeX XMLCite \textit{M. Bildhauer} and \textit{M. Fuchs}, Calc. Var. Partial Differ. Equ. 37, No. 1--2, 167--186 (2010; Zbl 1189.49057) Full Text: DOI
Fuchs, M.; Seregin, G. A global nonlinear evolution problem for generalized Newtonian fluids: Local initial regularity of the strong solution. (English) Zbl 1122.76008 Comput. Math. Appl. 53, No. 3-4, 509-520 (2007). MSC: 76A05 35Q35 PDFBibTeX XMLCite \textit{M. Fuchs} and \textit{G. Seregin}, Comput. Math. Appl. 53, No. 3--4, 509--520 (2007; Zbl 1122.76008) Full Text: DOI DOI
Bildhauer, M.; Fuchs, M.; Zhong, X. On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids. (English) Zbl 1129.35061 St. Petersbg. Math. J. 18, No. 2, 183-199 (2007) and Algebra Anal. 18, No. 2, 1-23 (2006). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 76D03 35B65 35J20 76D05 PDFBibTeX XMLCite \textit{M. Bildhauer} et al., St. Petersbg. Math. J. 18, No. 2, 183--199 (2007; Zbl 1129.35061) Full Text: DOI