Calculus of Variations and Geometric Measure Theory
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V. Bögelein - F. Duzaar - G. Mingione

The boundary regularity of non-linear parabolic systems II

created by mingione on 29 Sep 2012


Published Paper

Inserted: 29 sep 2012

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 27
Pages: 145–200
Year: 2010


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 we achieve dimension estimates for the boundary singular set and eventually the almost everywhere regularity of solutions at the boundary

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