Fachbereich Mathematik 
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Publications of Thomas Schmidt

Journal articles (with links to abstracts and preprint versions):

  1. Higher integrability for the gradient of Mumford-Shah almost-minimizers (with coauthor S. Piontek).
    ESAIM, Control Optim. Calc. Var. 26, 6, 20 pp. (2020).
  2. On the dual formulation of obstacle problems for the total variation and the area functional (with coauthor C. Scheven).
    Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, 1175-1207 (2018).
  3. BV supersolutions to equations of 1-Laplace and minimal surface type (with coauthor C. Scheven).
    J. Differ. Equations 261, 1904-1932 (2016).
  4. Interior gradient regularity for BV minimizers of singular variational problems (with coauthor L. Beck).
    Nonlinear Anal., Theory Methods Appl. 120, 86-106 (2015).
  5. Strict interior approximation of sets of finite perimeter and functions of bounded variation.
    Proc. Am. Math. Soc. 143, 2069-2084 (2015).
  6. Convex duality and uniqueness for BV-minimizers (with coauthor L. Beck).
    J. Funct. Anal. 268, 3061-3107 (2015).
  7. Partial regularity for mass-minimizing currents in Hilbert spaces (with coauthors L. Ambrosio, C. De Lellis).
    J. Reine Angew. Math. 734, 99-144 (2018).
  8. Partial regularity for degenerate variational problems and image restoration models in BV.
    Indiana Univ. Math. J. 63, 213-279 (2014).
  9. W2,1+ε estimates for the Monge-Ampère equation.
    Adv. Math. 240, 672-689 (2013).
  10. Compactness results for normal currents and the Plateau problem in dual Banach spaces (with coauthor L. Ambrosio).
    Proc. Lond. Math. Soc. (3) 106, 1121-1142 (2013).
  11. On the Dirichlet problem for variational integrals in BV (with coauthor L. Beck).
    J. Reine Angew. Math. 674, 113-194 (2013).
  12. Local and asymptotic regularity results for quasiconvex and quasimonotone problems (with coauthors M. Carozza, A. Passarelli di Napoli, A. Verde).
    Q. J. Math. 63, 325-352 (2012).
  13. Asymptotically regular problems II: Partial Lipschitz continuity and a singular set of positive measure (with coauthor C. Scheven).
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) VIII, 469-507 (2009).
  14. Asymptotically regular problems I: Higher integrability (with coauthor C. Scheven).
    J. Differ. Equations 248, 745-791 (2010).
  15. A simple partial regularity proof for minimizers of variational integrals.
    NoDEA, Nonlinear Differ. Equ. Appl. 16, 109-129 (2009).
  16. Partial regularity of strong local minimizers of quasiconvex integrals with (p,q)-growth (with coauthor S. Schemm).
    Proc. R. Soc. Edinb., Sect. A, Math. 139, 595-621 (2009).
  17. Regularity theorems for degenerate quasiconvex energies with (p,q)-growth.
    Adv. Calc. Var. 1, 241-270 (2008).
  18. Regularity of relaxed minimizers of quasiconvex variational integrals with (p,q)-growth.
    Arch. Ration. Mech. Anal. 193, 311-337 (2009).
  19. Regularity of minimizers of W1,p-quasiconvex variational integrals with (p,q)-growth.
    Calc. Var. Partial Differ. Equ. 32, 1-24 (2008).

Research announcements:


  Seitenanfang  Impress 2020-02-20, Thomas Schmidt