Fachbereich Mathematik 
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Publications of Thomas Schmidt

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

  1. 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).
  2. BV supersolutions to equations of 1-Laplace and minimal surface type (with coauthor C. Scheven).
    J. Differ. Equations 261, 1904-1932 (2016).
  3. Interior gradient regularity for BV minimizers of singular variational problems (with coauthor L. Beck).
    Nonlinear Anal., Theory Methods Appl. 120, 86-106 (2015).
  4. Strict interior approximation of sets of finite perimeter and functions of bounded variation.
    Proc. Am. Math. Soc. 143, 2069-2084 (2015).
  5. Convex duality and uniqueness for BV-minimizers (with coauthor L. Beck).
    J. Funct. Anal. 268, 3061-3107 (2015).
  6. Partial regularity for mass-minimizing currents in Hilbert spaces (with coauthors L. Ambrosio, C. De Lellis).
    J. Reine Angew. Math. 734, 99-144 (2018).
  7. Partial regularity for degenerate variational problems and image restoration models in BV.
    Indiana Univ. Math. J. 63, 213-279 (2014).
  8. W2,1+ε estimates for the Monge-Ampère equation.
    Adv. Math. 240, 672-689 (2013).
  9. 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).
  10. On the Dirichlet problem for variational integrals in BV (with coauthor L. Beck).
    J. Reine Angew. Math. 674, 113-194 (2013).
  11. 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).
  12. 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).
  13. Asymptotically regular problems I: Higher integrability (with coauthor C. Scheven).
    J. Differ. Equations 248, 745-791 (2010).
  14. A simple partial regularity proof for minimizers of variational integrals.
    NoDEA, Nonlinear Differ. Equ. Appl. 16, 109-129 (2009).
  15. 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).
  16. Regularity theorems for degenerate quasiconvex energies with (p,q)-growth.
    Adv. Calc. Var. 1, 241-270 (2008).
  17. Regularity of relaxed minimizers of quasiconvex variational integrals with (p,q)-growth.
    Arch. Ration. Mech. Anal. 193, 311-337 (2009).
  18. 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 2018-06-14, Thomas Schmidt