Equivalence of viscosity and weak solutions for the p(x)-Laplacian

被引：30

作者：

Juutinen, Petri ^{[1
]}

Lukkari, Teemu ^{[2
]}

Parviainen, Mikko ^{[3
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, FIN-40014 Jyvaskyla, Finland

[2] NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

[3] Aalto Univ, Sch Sci & Technol, Inst Math, FI-00076 Aalto, Finland

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2010年 / 27卷 / 06期

关键词：

Comparison principle; Viscosity solutions Uniqueness p(lambda); Superharmonic functions; Rado type theorem Removability; FUNCTIONALS;

D O I：

10.1016/j.anihpc.2010.09.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider different notions of solutions to the p(lambda) Laplace equation -div(vertical bar Du(x)vertical bar(p(lambda)-2) Du(x)) = 0 with 1 < p(x) < infinity We show by proving a comparison principle that viscosity supersolutions and p(x)-superharmonic functions of nonlinear potential theory coincide This implies that weak and viscosity solutions are the same class of functions and that viscosity solutions to Dirichlet problems are unique As an application we prove a Rado type removability theorem (C) 2010 Elsevier Masson SAS All rights reserved

引用

页码：1471 / 1487

页数：17

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