Equivalence of solutions to fractional p-Laplace type equations

被引：50

作者：

Korvenpaa, Janne ^{[1
]}

Kuusi, Tuomo ^{[1
]}

Lindgren, Erik ^{[2
]}

机构：

[1] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland

[2] KTH, Dept Math, S-10044 Stockholm, Sweden

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 132卷

基金：

芬兰科学院; 瑞典研究理事会;

关键词：

Nonlocal operators; Fractional Sobolev spaces; Fractional p-Laplacian; Viscosity solutions; VISCOSITY SOLUTIONS; WEAK;

D O I：

10.1016/j.matpur.2017.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study different notions of solutions of nonlocal and nonlinear equations of fractional p-Laplace type P.V. integral(Rn)vertical bar u(x) - u(y)vertical bar(p-2)(u(x) - u(y))/vertical bar x-y vertical bar(n+sp) dy = 0. Solutions are defined via integration by parts with test functions, as viscosity solutions or via comparison. Our main result states that for bounded solutions, the three different notions coincide. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：1 / 26

页数：26

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