OPTIMAL GRADIENT ESTIMATES VIA RIESZ POTENTIALS FOR p(•)-LAPLACIAN TYPE EQUATIONS

被引：14

作者：

Byun, Sun-Sig ^{[1
,2
]}

Youn, Yeonghun ^{[1
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2017年 / 68卷 / 04期

关键词：

SOBOLEV EMBEDDINGS;

D O I：

10.1093/qmath/hax013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate degenerate elliptic equations with coefficients of p(center dot)-Laplacian type when the right-hand side is a finite Borel measure. An optimal pointwise estimate of the gradient of a very weak solution to such a measure data problem is obtained via a Riesz potential of the measure under a minimal regularity requirement on the associated coefficients and an optimal condition on the variable exponent p(center dot). As a consequence, we are able to derive a C-1 regularity criterion as well as a Calderon-Zygmund-type estimate in the literature.

引用

页码：1071 / 1115

页数：45

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