Regularity Results for Nonlocal Equations by Approximation

被引：173

作者：

Caffarelli, Luis ^{[1
]}

Silvestre, Luis ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2011年 / 200卷 / 01期

关键词：

INTEGRODIFFERENTIAL EQUATIONS;

D O I：

10.1007/s00205-010-0336-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain C (1,alpha) regularity estimates for nonlocal elliptic equations that are not necessarily translation-invariant using compactness and perturbative methods and our previous regularity results for the translation-invariant case.

引用

页码：59 / 88

页数：30

共 9 条

[1]

[Anonymous], 1954, Annals of Mathematics Studies

[2]

[Anonymous], 1995, Fully nonlinear elliptic equations

[3]

BARLES G, J EUR MATH IN PRESS

[4] INTERIOR A PRIORI ESTIMATES FOR SOLUTIONS OF FULLY NON-LINEAR EQUATIONS [J].

CAFFARELLI, LA .

ANNALS OF MATHEMATICS, 1989, 130 (01) :189-213

[5] Regularity Theory for Fully Nonlinear Integro-Differential Equations [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (05) :597-638

[6] UBER DIE ERSTE RANDWERTAUFGABE BEI QUASILINEAREN DIFFERENTIALGLEICHUNGEN ZWEITER ORDNUNG IN MEHR ALS ZWEI VARIABLEN [J].

CORDES, HO .

MATHEMATISCHE ANNALEN, 1956, 131 (03) :278-312

[7] A priori estimates for integro-differential operators with measurable kernels [J].

Kassmann, Moritz .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (01) :1-21

[8]

MIKULYAVICHYUS R, 1996, LIET MAT RINK, V36, P178

[9] Holder estimates for solutions of integro-differential equations like the fractional Laplace [J].

Silvestre, Luis .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (03) :1155-1174

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