Comparison results for nonlinear divergence structure elliptic PDE's

Yichen Liu; Monica Marras; Giovanni Porru

doi:10.1515/anona-2020-0008

Comparison results for nonlinear divergence structure elliptic PDE's

Yichen Liu^*, Monica Marras, Giovanni Porru

^*Corresponding author for this work

Department of Applied Mathematics

University of Cagliari

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	438-448
Number of pages	11
Journal	Advances in Nonlinear Analysis
Volume	9
Issue number	1
DOIs	https://doi.org/10.1515/anona-2020-0008
Publication status	Published - 1 Mar 2019

Keywords

Comparison results
Quasi-linear equations
Symmetrization

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10.1515/anona-2020-0008

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abstract = "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.",

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AB - 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.

KW - Comparison results

KW - Quasi-linear equations

KW - Symmetrization

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Comparison results for nonlinear divergence structure elliptic PDE's

Abstract

Keywords

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