Remarks on regularity for p-Laplacian type equations in non-divergence form

被引：26

作者：

Attouchi, Amal ^{[1
]}

Ruosteenoja, Eero ^{[1
]}

机构：

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 265卷 / 05期

基金：

芬兰科学院;

关键词：

p-Laplacian; Viscosity solutions; Local C-1; C-alpha regularity; Integrability of second derivatives; VISCOSITY SOLUTIONS; BOUNDARY-REGULARITY; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; WEAK SOLUTIONS; EQUIVALENCE; SYSTEMS; SETS;

D O I：

10.1016/j.jde.2018.04.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a singular or degenerate equation in non-divergence form modeled on the p-Laplacian, -vertical bar Du vertical bar(gamma) (Delta u + (p -2)Delta(N)(infinity)u) = f in Omega. We investigate local C-1,C-alpha regularity of viscosity solutions in the full range gamma > -1 and p > 1, and provide local W-2,W-2 estimates in the restricted cases where p is close to 2 and gamma is close to 0. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1922 / 1961

页数：40

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