Neumann problem for p-Laplace equation in metric spaces using a variational approach: Existence, boundedness, and boundary regularity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Maly, Lukas¹  Shanmugalingam, Nageswari¹ 

[1] Univ Cincinnati, Dept Math Sci, POB 210025, Cincinnati, OH 45215 USA

关键词: p-Laplace equation;    Neumann boundary value problem;    Metric measure space;    Variational problem;    Boundary regularity;    De Giorgi type inequality;   

DOI  :  10.1016/j.jde.2018.04.038

来源: Elsevier

【 摘 要 】

We employ a variational approach to study the Neumann boundary value problem for the p-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel measurable bounded functions. We also study boundary continuity properties of the solutions. One of the key tools utilized is the trace theorem for Newton-Sobolev functions, and another is an analog of the De Giorgi inequality adapted to the Neumann problem. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free