C1,α regularity for the normalized p-Poisson problem

被引：36

作者：

Attouchi, Amal ^{[1
]}

Parviainen, Mikko ^{[1
]}

Ruosteenoja, Eero ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2017年 / 108卷 / 04期

基金：

芬兰科学院;

关键词：

Normalized p-Laplacian; p-Poisson problem; Viscosity solutions; Local C-1; C-alpha regularity; TUG-OF-WAR; VISCOSITY SOLUTIONS; WEAK SOLUTIONS; EQUIVALENCE; LAPLACIAN; EQUATION; PROOF;

D O I：

10.1016/j.matpur.2017.05.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the normalized p-Poisson problem Delta(N)(p)u = f in Omega subset of R-n. The normalized p -Laplacian Delta(N)(p)u := vertical bar Du vertical bar(2-P)Delta(p)u is in non -divergence form and arises for example from stochastic games. We prove C-loc(1-alpha) regularity with nearly optimal alpha for viscosity solutions of this problem. In the case f is an element of L-infinity boolean AND C and p > 1 we use methods both from viscosity and weak theory, whereas in the case f is an element of L-q boolean AND C, q > max(n, E/2, 2), and p > 2 we rely on the tools of nonlinear potential theory. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：553 / 591

页数：39

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