Partial Holder continuity for discontinuous elliptic problems with VMO-coefficients

被引:41
|
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
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
收藏
页码:371 / 404
页数:34
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