Comparison results for nonlinear divergence structure elliptic PDE’s

Comparison results for nonlinear divergence structure elliptic PDE’s

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 measur...

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Bibliographic Details
Main Authors: Liu Yichen, Marras Monica, Porru Giovanni
Format: Article
Language:English
Published: De Gruyter 2019-06-01
Series:Advances in Nonlinear Analysis
Subjects:
quasi-linear equations
symmetrization
comparison results
35b51
35j62
49k20
49k30
Online Access:https://doi.org/10.1515/anona-2020-0008
Description
Summary: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.
ISSN:2191-950X

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