JournalsaihpcVol. 27, No. 1pp. 201–255

The boundary regularity of non-linear parabolic systems I

  • 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
The boundary regularity of non-linear parabolic systems I cover
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Abstract

This is the first 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 develop the basic necessary and sufficient condition for establishing the regular nature of a boundary point.

Cite this article

Verena Bögelein, Frank Duzaar, Giuseppe Mingione, The boundary regularity of non-linear parabolic systems I. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 1, pp. 201–255

DOI 10.1016/J.ANIHPC.2009.09.003