Comparison results for nonlinear divergence structure elliptic PDE’s

Advances in Nonlinear Analysis

article

Yichen Liu¹  Monica Marras²  Giovanni Porru² 

[1] Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University;Department of Mathematics and Informatics, University of Cagliari

关键词: Quasi-linear equations;    Symmetrization;    Comparison results;   

DOI  :  10.1515/anona-2020-0008

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω . For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

【 授权许可】

CC BY