Universität des Saarlandes  

Department
of Mathematics


Publications Michael Bildhauer, update: Oct. 2023


  1. Bildhauer, Michael; Fuchs, Martin.

    Splitting-type variational problems with asymmetrical growth conditions.

    To appear in Bollettino dell'Unione Matematica Italiana.

  2. Bildhauer, Michael; Farquhar, Bernhard; Fuchs, Martin.

    A small remark on Bernstein's theorem.

    Arch. Math. (Basel) 121 (2023), no. 4, 437-447.

  3. 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.

    J. Elliptic Parabol. Equ. 8 (2022), no. 2, 853-884.

  4. Bildhauer, Michael; Fuchs, Martin.

    Small weights in Caccioppoli's inequality and applications to Liouville-type theorems for non-standard problems.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 508 (2021), Kraevye Zadachi Matematicheskoĭ Fiziki i Smeszhnye Voprosy Teorii Funktsiĭ. 49, 73–88.

  5. Bildhauer, Michael; Fuchs, Martin.

    An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler-Lagrange equations related to general linear growth problems.

    Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 99, 8 pp.

  6. Bildhauer, Michael; Fuchs, Martin.

    Some geometric properties of nonparametric $\mu$-surfaces in $\rz^3$.

    Journal of Geometric Analysis 32 (2022), no. 4, Paper No. 113, 20 pp.

  7. Bildhauer, Michael; Fuchs, Martin.

    Liouville-type results in two dimensions for stationary points of functionals with linear growth.

    Ann. Fenn. Math. 47 (2022), no. 1, 417-426.

  8. Bildhauer, Michael; Fuchs, Martin.

    Splitting-type variational problems with mixed linear- superlinear growth conditions.

    J. Math. Anal. Appl. 501 (2021), no. 1, 29 pp.

  9. Bildhauer, Michael; Fuchs, Martin.

    Splitting type variational problems with linear growth conditions.

    J. Math. Sci. (N.Y.) 250 (2020), no. 2, Problems in mathematical analysis. No. 105, 232-249.

  10. Bildhauer, Michael.

    Einführung in die Mathematik für Ingenieure und Naturwissenschaftler Teil 1.

    Preprint 405, Department of Mathematics, Saarland University, 2020.

  11. Bildhauer, Michael; Fuchs, Martin.

    On a class of variational problems with linear growth and radial symmetry.

    Comment. Math. Univ. Carolin. 62 (2021), no. 3, 325-345.

  12. Bildhauer, Michael; Fuchs, Martin.

    Existence results for denoising problems with generalized edge-enhancing diffusion.

    J. Math. Sci. (N.Y.) 244 (2020), no. 3, Problems in mathematical analysis. No. 100, 390–400.

  13. Bildhauer, Michael; Cardenas, Marcelo; Fuchs, Martin; Weickert, Joachim.

    Existence Theory for the EED Inpainting Problem.

    Algebra i Analiz 32 (2020), no. 3, 127-148.

  14. Bildhauer, Michael; Fuchs, Martin; Müller, Jan.

    Existence and regularity for stationary incompressible flows with dissipative potentials of linear growth.

    J. Math. Fluid Mech. 20 (2018), no. 4, 1567-1587.

  15. Bildhauer, Michael; Fuchs, Martin; Müller, Jan.

    A reciprocity principle for constrained isoperimetric problems and existence of isoperimetric regions in convex sets.

    Calc. Var. Partial Differential Equations 57 (2018), no. 2, 12 pp.

  16. Bildhauer, Michael; Fuchs, Martin; Müller, Jan; Zhong, Xiao.

    On the local boundedness of generalized minimizers of variational problems with linear growth.

    Ann. Mat. Pura Appl. (4) 197 (2018), no. 4, 1117-1129.

  17. Bildhauer, Michael; Fuchs, Martin; Müller, Jan; Tietz, Christian.

    On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case.

    J. Elliptic Parabol. Equ. 2 (2016), no. 1-2, 341-355.

  18. Bildhauer, Michael; Fuchs, Martin; Weickert, Joachim.

    Denoising and inpainting of images using TV-type energies: theoretical and computational aspects.

    J. Math. Sci. (N.Y.) 219 (2016), no. 6, Problems in mathematical analysis. No. 87 (Russian), 899-910.

  19. Bildhauer, Michael; Fuchs, Martin.

    Some remarks on the (non-) attainment of the boundary data for variational problems in the space BV.

    J. Convex Anal. 25 (2018), no. 1, 219-223.

  20. Bildhauer, Michael; Fuchs, Martin; Weickert, Joachim.

    An alternative approach towards the higher order denoising of images. Analytical aspects.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 444 (2016), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 45, 47-88; translation in J. Math. Sci. (N.Y.) 224 (2017), no. 3, 414-441.

  21. Bildhauer, Michael; Fuchs, Martin; Tietz, Christian.

    C1a-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting.

    Algebra i Analiz 27 (2015), no. 3, 51-65; translation in St. Petersburg Math. J. 27 (2016), no. 3, 381-392.

  22. Bildhauer, Michael; Fuchs, Martin.

    Image inpainting with energies of linear growth - a collection of proposals.

    J. Math. Sci. (N.Y.) 196 (2014), no. 4, Problems in mathematical analysis. No. 74 (Russian), 490-497.

  23. Bildhauer, Michael; Fuchs, Martin.

    On some perturbations of the total variation image inpainting method. Part III: minimization among sets with finite perimeter.

    J. Math. Sci. (N.Y.) 207 (2015), no. 2, Problems in mathematical analysis. No. 78 (Russian), 142-146.

  24. Bildhauer, Michael; Fuchs, Martin.

    On some perturbations of the total variation image inpainting method. Part II: relaxation and dual variational formulation.

    J. Math. Sci. (N.Y.) 205 (2015), no. 2, Problems in mathematical analysis. No. 77 (Russian), 121-140.

  25. Bildhauer, Michael; Fuchs, Martin.

    On some perturbations of the total variation image inpainting method. Part I: regularity theory.

    J. Math. Sci. (N.Y.) 202 (2014), no. 2, Problems in mathematical analysis. No. 76 (Russian), 154-169.

  26. Bildhauer, Michael; Fuchs, Martin; Zhang, Guo.

    Liouville-type theorems for steady flows of degenerate power law fluids in the plane.

    J. Math. Fluid Mech. 15 (2013), no. 3, 583-616.

  27. Bildhauer, Michael; Naumann, Joachim; Wolf, J\''org.

    An approximation theorem for vector fields in BD_div.

    Preprint 311, Department of Mathematics, Saarland University, 2012.

  28. Bildhauer, Michael; Fuchs, Martin.

    Lipschitz regularity for constrained local minimizers of convex variational integrals with a wide range of anisotropy.

    Manuscripta Math. 141 (2013), no. 1-2, 63-83.

  29. Bildhauer, Michael; Fuchs, Martin.

    On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity.

    Comment. Math. Univ. Carolin. 53 (2012), no. 2, 221-236.

  30. Bildhauer, Michael; Fuchs, Martin.

    A variational approach to the denoising of images based on different variants of the TV-regularization.

    Appl. Math. Optim. 66 (2012), no. 3, 331-361.

  31. Bildhauer, Michael; Fuchs, Martin.

    Compact embeddings of the space of functions with bounded logarithmic deformation.

    Problems in mathematical analysis. No. 51. J. Math. Sci. (N.Y.) 172 (2011), no. 1, 165-183.

  32. Bildhauer, Michael; Fuchs, Martin.

    A 2D-variant of a theorem of Uraltseva and Urdaletova for higher-order variational problems.

    Nonlinear partial differential equations and related topics, 39–49, Amer. Math. Soc. Transl. Ser. 2, 229, Adv. Math. Sci., 64, Amer. Math. Soc., Providence, RI, 2010.

  33. 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.

    Calc. Var. Partial Differential Equations 37 (2010), no. 1-2, 167-186.

  34. Apushkinskaya, Darya; Bildhauer, Michael; Fuchs, Martin.

    On local generalized minimizers and local stress tensors for variational problems with linear growth.

    Problems in mathematical analysis. No. 44. J. Math. Sci. (N.Y.) 165 (2010), no. 1, 42-59.

  35. Bildhauer, Michael; Fuchs, Martin.

    A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 385 (2010), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 41, 5-17, 234; translation in J. Math. Sci. (N.Y.) 178 (2011), no. 3, 235-242.

  36. Bildhauer, Michael; Fuchs, Martin; Repin, Sergey.

    The elastic-plastic torsion problem: a posteriori error estimates for approximate solutions.

    Numer. Funct. Anal. Optim. 30 (2009), no. 7-8, 653-664.

  37. Apushkinskaya, Darya; Bildhauer, Michael; Fuchs, Martin.

    Interior gradient bounds for local minimizers of variational integrals under nonstandard growth conditions.

    Problems in mathematical analysis. No. 43. J. Math. Sci. (N.Y.) 164 (2010), no. 3, 345-363.

  38. Bildhauer, Michael; Fuchs, Martin.

    Variational integrals of splitting-type: higher integrability under general growth conditions.

    Ann. Mat. Pura Appl. (4) 188 (2009), no. 3, 467-496.

  39. Bildhauer, Michael; Fuchs, Martin.

    Error estimates for obstacle problems of higher order.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 348 (2007), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 38, 5-18, 303; translation in J. Math. Sci. (N.Y.) 152 (2008), no. 5, 617-624.

  40. Bildhauer, Michael; Fuchs, Martin.

    A remark on the regularity of vector-valued mappings depending on two variables which minimize splitting-type variational integrals.

    Acta Math. Sci. Ser. B Engl. Ed. 30 (2010), no. 3, 963-967.

  41. Bildhauer, Michael; Fuchs, Martin; Repin, Sergey.

    Duality based a posteriori error estimates for higher order variational inequalities with power growth functionals.

    Ann. Acad. Sci. Fenn. Math. 33 (2008), no. 2, 475-490.

  42. Bildhauer, Michael; Fuchs, Martin.

    Partial regularity for local minimizers of splitting-type variational integrals.

    Asymptot. Anal. 55 (2007), no. 1-2, 33-47.

  43. Bildhauer, Michael; Fuchs, Martin; Repin, Sergey.

    A functional type a posteriori error analysis for the Ramberg-Osgood model.

    ZAMM Z. Angew. Math. Mech. 87 (2007), no. 11-12, 860-876.

  44. Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao.

    A regularity theory for scalar local minimizers of splitting-type variational integrals.

    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), no. 3, 385-404.

  45. Bildhauer, Michael; Fuchs, Martin.

    Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals.

    Manuscripta Math. 123 (2007), no. 3, 269-283.

  46. Bildhauer, Michael; Fuchs, Martin.

    On the regularity of local minimizers of decomposable variational integrals on domains in R^2.

    Comment. Math. Univ. Carolin. 48 (2007), no. 2, 321-341.

  47. Bildhauer, Michael; Fuchs, Martin.

    Continuity properties of the stress tensor in the 3-dimensional Ramberg/Osgood model.

    J. Appl. Anal. 13 (2007), no. 2, 209-233.

  48. Bildhauer, Michael; Fuchs, Martin.

    Smoothness of weak solutions of the Ramberg/Osgood equations on plane domains.

    ZAMM Z. Angew. Math. Mech. 87 (2007), no. 1, 70-76.

  49. Bildhauer, Michael; Fuchs, Martin.

    A short remark on energy functionals related to nonlinear Hencky materials.

    Appl. Math. E-Notes 7 (2007), 77-83.

  50. Bildhauer, Michael; Repin, Sergey.

    Estimates of the deviation from the minimizer for variational problems with power growth functionals.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 336 (2006), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 37, 5-24, 274; translation in J. Math. Sci. (N.Y.) 143 (2007), no. 2, 2845-2856.

  51. Bildhauer, Michael; Fuchs, Martin.

    Higher order variational problems on two-dimensional domains.

    Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 2, 349-362.

  52. Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao.

    Variational integrals with a wide range of anisotropy.

    Algebra i Analiz 18 (2006), no. 5, 46-71; translation in St. Petersburg Math. J. 18 (2007), no. 5, 717-736

  53. Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao.

    On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids.

    Algebra i Analiz 18 (2006), no. 2, 1-23; translation in St. Petersburg Math. J. 18 (2007), no. 2, 183-199.

  54. Bildhauer, Michael; Fuchs, Martin.

    C1,a-solutions to non-autonomous anisotropic variational problems.

    Calc. Var. Partial Differential Equations 24 (2005), no. 3, 309-340.

  55. Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao.

    A lemma on the higher integrability of functions with applications to the regularity theory of two-dimensional generalized Newtonian fluids.

    Manuscripta Math. 116 (2005), no. 2, 135-156.

  56. Bildhauer, Michael; Fuchs, Martin.

    Regularization of convex variational problems with applications to generalized Newtonian fluids.

    Arch. Math. (Basel) 84 (2005), no. 2, 155-170.

  57. Apushkinskaya, Darya; Bildhauer, Michael; Fuchs, Martin.

    Steady states of anisotropic generalized Newtonian fluids.

    J. Math. Fluid Mech. 7 (2005), no. 2, 261-297.

  58. Bildhauer, Michael; Fuchs, Martin.

    A regularity result for stationary electrorheological fluids in two dimensions.

    Math. Methods Appl. Sci. 27 (2004), no. 13, 1607-1617.

  59. Bildhauer, Michael; Fuchs, Martin.

    Variants of the Stokes problem: the case of anisotropic potentials.

    J. Math. Fluid Mech. 5 (2003), no. 4, 364-402.

  60. Bildhauer, Michael.

    Two dimensional variational problems with linear growth.

    Manuscripta Math. 110 (2003), no. 3, 325-342.

  61. Bildhauer, Michael.

    Convex variational problems. Linear, nearly linear and anisotropic growth conditions.

    Lecture Notes in Mathematics, 1818. Springer-Verlag, Berlin, 2003.

  62. Bildhauer, Michael.

    Convex variational integrals with a wide range of anisotropy. Part II: mixed linear/superlinear growth conditions.

    Preprint 55, Department of Mathematics, Saarland University, 2002.

  63. Bildhauer, Michael; Fuchs, Martin.

    Interior regularity for free and constrained local minimizers of variational integrals under general growth and ellipticity conditions.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 288 (2002), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 32, 79-99, 271-272; translation in J. Math. Sci. (N.Y.) 123 (2004), no. 6, 4565-4576.

  64. Bildhauer, Michael; Fuchs, Martin.

    Elliptic variational problems with nonstandard growth.

    Nonlinear problems in mathematical physics and related topics, I, 53-66, Int. Math. Ser. (N. Y.), 1, Kluwer/Plenum, New York, 2002.

  65. Bildhauer, Michael; Fuchs, Martin.

    Convex variational problems with linear growth.

    Geometric analysis and nonlinear partial differential equations, 327-344, Springer, Berlin, 2003.

  66. Bildhauer, Michael; Fuchs, Martin.

    Twodimensional anisotropic variational problems.

    Calc. Var. Partial Differential Equations 16 (2003), no. 2, 177-186.

  67. Bildhauer, Michael.

    Convex variational integrals with a wide range of anisotropy. Part I: regularity results.

    Preprint 40, Department of Mathematics, Saarland University, 2001.

  68. Bildhauer, Michael; Fuchs, Martin.

    Partial regularity for a class of anisotropic variational integrals with convex hull property.

    Asymptot. Anal. 32 (2002), no. 3-4, 293-315.

  69. Bildhauer, Michael; Fuchs, Martin.

    Relaxation of convex variational problems with linear growth defined on classes of vector-valued functions.

    Algebra i Analiz 14 (2002), no. 1, 26-45; translation in St. Petersburg Math. J. 14 (2003), no. 1, 19-33.

  70. Bildhauer, Michael.

    A note on degenerate variational problems with linear growth.

    Z. Anal. Anwendungen 20 (2001), no. 3, 589-598.

  71. Bildhauer, Michael.

    A priori gradient estimates for bounded generalized solutions of a class of variational problems with linear growth.

    J. Convex Anal. 9 (2002), no. 1, 117-137.

  72. Bildhauer, Michael; Fuchs, Martin; Osmolovskii, Victor.

    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.

    Math. Methods Appl. Sci. 25 (2002), no. 4, 289-308.

  73. Bildhauer, Michael; Fuchs, Martin; Osmolovskii, Victor.

    The effect of a surface energy term on the distribution of phases in an elastic medium with a two-well elastic potential.

    Math. Methods Appl. Sci. 25 (2002), no. 2, 149-178.

  74. Bildhauer, Michael; Fuchs, Martin.

    Partial regularity for variational integrals with (s,\mu,q)-growth.

    Calc. Var. Partial Differential Equations 13 (2001), no. 4, 537-560.

  75. Bildhauer, Michael; Fuchs, Martin.

    On a class of variational integrals with linear growth satisfying the condition of \mu-ellipticity.

    Rend. Mat. Appl. (7) 22 (2002), 249-274 (2003).

  76. Bildhauer, Michael; Fuchs, Martin; Mingione, Giuseppe.

    A priori gradient bounds and local C1,a-estimates for (double) obstacle problems under non-standard growth conditions.

    Z. Anal. Anwendungen 20 (2001), no. 4, 959-985.

  77. Bildhauer, Michael; Fuchs, Martin; Seregin, Gregory.

    Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body.

    NoDEA Nonlinear Differential Equations Appl. 8 (2001), no. 1, 53-81.

  78. Bildhauer, Michael; Fuchs, Martin.

    Higher order variational inequalities with non-standard growth conditions in dimension two: plates with obstacles.

    Ann. Acad. Sci. Fenn. Math. 26 (2001), no. 2, 509-518.

  79. Bildhauer, Michael.

    A uniqueness theorem for the dual problem associated to a variational problem with linear growth.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 271 (2000), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 31, 83-91, 314-315; translation in J. Math. Sci. (N. Y.) 115 (2003), no. 6, 2747-2752

  80. Bildhauer, Michael; Fuchs, Martin.

    Obstacle problems with linear growth: Hölder regularity for the dual solution.

    Math. Nachr. 232 (2001), 5-27.

  81. Bildhauer, Michael; Fuchs, Martin.

    Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth.

    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 259 (1999), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 30, 46-66, 296; translation in J. Math. Sci. (New York) 109 (2002), no. 5, 1835-1850.

  82. Bildhauer, Michael.

    A remark on isolated singularities of surfaces with bounded mean curvature: the non-minimizing and non-perpendicular case.

    Arch. Math. (Basel) 75 (2000), no. 2, 153-160.

  83. Bildhauer, Michael.

    On the free boundary of surfaces with bounded mean curvature: the non-perpendicular case.

    Manuscripta Math. 97 (1998), no. 3, 389-406.

  84. Bildhauer, Michael.

    On the Hausdorff dimension of n x m concentration sets.

    Asymptotic Anal. 11 (1995), no. 2, 169-184.