JournalsaihpcVol. 27, No. 1pp. 145–200

The boundary regularity of non-linear parabolic systems II

  • Verena Bögelein

    Department Mathematik, Universität Erlangen–Nürnberg, Bismarckstrasse 1 1/2, 91054 Erlangen, Germany

  • Frank Duzaar

    Department Mathematik, Universität Erlangen–Nürnberg, Bismarckstrasse 1 1/2, 91054 Erlangen, Germany

  • Giuseppe Mingione

    Dipartimento Mathematica, Università di Parma, Parco delle Scienze 53/a, Campus, 43100 Parma, Italy
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Abstract

This is the second part of a work aimed at establishing that for solutions to Cauchy–Dirichlet problems involving general non-linear systems of parabolic type, almost every parabolic boundary point is a Hölder continuity point for the spatial gradient of solutions. Here we establish higher fractional differentiability of solutions up to the boundary. Based on the necessary and sufficient condition for regular boundary points from the first part of Bögelein et al. (in this issue)[7] we achieve dimension estimates for the boundary singular set and eventually the almost everywhere regularity of solutions at the boundary.

Cite this article

Verena Bögelein, Frank Duzaar, Giuseppe Mingione, The boundary regularity of non-linear parabolic systems II. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 1, pp. 145–200

DOI 10.1016/J.ANIHPC.2009.09.002