The viscosity solutions of a nonlinear equation related to the p-Laplacian

AIMS Mathematics

关键词: : ;    Nonlinear equation;    p-Laplacian;    moser iteration;    viscosity solution;   

DOI  :  10.3934/Math.2017.3.400

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

The viscosity solutions of a nonlinear equation related to the p-Laplacian are considered. Besides there is a damping term in the equation, a nonlocal function is added. By considering the regularized problem and using Moser iteration technique, we get the uniformly local bounded properties of the solutions and the L^p-norm for the gradients. By the compactness theorem, we prove the existence of the viscosity solution of the equation.

【 授权许可】

CC BY