The boundary regularity of non-linear parabolic systems II

Bögelein V, Duzaar F, Mingione G (2010)

Publication Type: Journal article

Publication year: 2010

Journal

Annales de l'Institut Henri Poincaré - Analyse Non Linéaire Elsevier Masson / Institute Henri Poincaré

Book Volume: 27

Pages Range: 145-200

Journal Issue: 1

URI: https://www.sciencedirect.com/science/article/pii/S0294144909000833?via=ihub

DOI: 10.1016/j.anihpc.2009.09.002

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.

Authors with CRIS profile

Verena Anna Maria Bögelein
Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

University of Parma / Università degli Studi di Parma IT Italy (IT)

How to cite

APA:

Bögelein, V., Duzaar, F., & Mingione, G. (2010). The boundary regularity of non-linear parabolic systems II. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 27(1), 145-200. https://dx.doi.org/10.1016/j.anihpc.2009.09.002

MLA:

Bögelein, Verena, Frank Duzaar, and Giuseppe Mingione. "The boundary regularity of non-linear parabolic systems II." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 27.1 (2010): 145-200.

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