Non-local gradient dependent operators

被引：96

作者：

Bjorland, C. ^{[1
]}

Caffarelli, L. ^{[1
]}

Figalli, A. ^{[1
]}

机构：

[1] UT Austin Math, Austin, TX 78712 USA

来源：

ADVANCES IN MATHEMATICS | 2012年 / 230卷 / 4-6期

基金：

美国国家科学基金会;

关键词：

Quasilinear non-local operators; Tug-of-war; Existence; Regularity; TUG-OF-WAR; VISCOSITY SOLUTIONS; WEAK SOLUTIONS; REGULARITY;

D O I：

10.1016/j.aim.2012.03.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study a general class of "quasilinear non-local equations" depending on the gradient which arises from tug-of-war games. We establish a C-alpha/C-1,C-alpha/C-2,C-alpha. regularity theory for these equations (the kind of regularity depending on the assumptions on the kernel), and we construct different non-local approximations of the p-Laplacian. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1859 / 1894

页数：36

共 16 条

[1]

[Anonymous], HOLDER INFINITE LAPL

[2]

[Anonymous], 1995, Fully nonlinear elliptic equations

[3] Nonlocal Tug-of-War and the Infinity Fractional Laplacian [J].