Sharp estimates for solutions to elliptic problems with mixed boundary conditions

被引：14

作者：

Alvino, A. ^{[1
]}

Chiacchio, F. ^{[1
]}

Nitsch, C. ^{[1
]}

Trombetti, C. ^{[1
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Complesso Univ Monte S Angelo,Via Cintia, Naples, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2021年 / 152卷

关键词：

A priori estimates; Comparison principle; Mixed boundary conditions; Robin boundary conditions;

D O I：

10.1016/j.matpur.2020.12.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on L-1 comparison) between solutions to an elliptic partial differential equation on a smooth bounded set Omega with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as Omega. This includes for instance mixed problems where Dirichlet boundary conditions are prescribed on part of the boundary, while Robin boundary conditions are prescribed on its complement. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页码：251 / 261

页数：11

共 15 条

[1] Convex symmetrization and applications [J].