Regularity theory for nonlocal equations with VMO coefficients

被引：12

作者：

Nowak, Simon ^{[1
]}

机构：

[1] Univ Bielefeld, Fak Math, Postfach 100131, D-33501 Bielefeld, Germany

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2023年 / 40卷 / 01期

关键词：

Nonlocal operator; nonlocal equations; Sobolev regularity; H?lder regularity; Calder?n-Zygmund estimates; ELLIPTIC-EQUATIONS; HOLDER REGULARITY; DIVERGENCE FORM; LAPLACIANS; DEGENERATE; SOBOLEV;

D O I：

10.4171/AIHPC/37

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove higher regularity for nonlinear nonlocal equations with possibly discontinu-ous coefficients of VMO type in fractional Sobolev spaces. While for corresponding local elliptic equations with VMO coefficients it is only possible to obtain higher integrability, in our nonlocal setting we are able to also prove a substantial amount of higher differentiability, so that our result is in some sense of purely nonlocal type. By embedding, we also obtain higher Holder regularity for such nonlocal equations.

引用

页码：61 / 132

页数：72

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