Partial continuity for elliptic problems

被引：54

作者：

Foss, Mikil ^{[2
]}

Mingione, Giuseppe ^{[1
]}

机构：

[1] Univ Parma, Dipartimento Matemat, I-43100 Parma, Italy

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2008年 / 25卷 / 03期

关键词：

partial regularity; elliptic systems; quasiconvexity;

D O I：

10.1016/j.anihpc.2007.02.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the partial Holder continuity for solutions to elliptic systems and for minimizers of quasi-convex integrals, under the assumption of continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional measuring the oscillations in the solution and its gradient. To establish the decay estimate, we use the technique of A-harmonic approximation, based on Duzaar and Steffen's A-harmonic approximation lemma [F Duzaar, K. Steffen, Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, J. Reine Angew. Math. (Crelles J.) 546 (2002) 73-138]. (c) 2007 Elsevier Masson SAS. All rights reserved.

引用

页码：471 / 503

页数：33

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