Partial Holder continuity for discontinuous elliptic problems with VMO-coefficients

被引：43

作者：

Boegelein, Verena ^{[1
]}

Duzaar, Frank ^{[2
]}

Habermann, Jens ^{[1
]}

Scheven, Christoph ^{[2
]}

机构：

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

[2] Univ Erlangen Nurnberg, Dept Math, D-91054 Erlangen, Germany

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2011年 / 103卷

关键词：

PARTIAL REGULARITY; VARIATIONAL INTEGRALS; BOUNDARY-REGULARITY; OPTIMAL INTERIOR; SYSTEMS; MINIMIZERS; FUNCTIONALS; ORDER;

D O I：

10.1112/plms/pdr009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish partial Holder continuity for vector-valued solutions u : Omega -> R-N to elliptic systems of the type div a(x, u, Du) = 0 in Omega, as well as for minimizers u : Omega -> R-N of quasi-convex functionals F[u] := integral(Omega) f(x, u, Du) dx, where the structure function a, respectively, the integrand f is possibly discontinuous with respect to x. More precisely, we merely impose a uniform VMO-condition with respect to the x-dependence and continuity with respect to the u-dependence and prove Holder continuity of the solutions, respectively, the minimizers outside of a negligible set.

引用

页码：371 / 404

页数：34

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