Schwarz symmetrization and comparison results for nonlinear elliptic equations and eigenvalue problems

被引：3

作者：

Bonorino, Leonardo Prange ^{[1
]}

Bezerra Montenegro, Jose Fabio ^{[2
]}

机构：

[1] Univ Fed Rio Grande do Sul, Dept Matemat Pura & Aplicada, BR-91509900 Porto Alegre, RS, Brazil

[2] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2013年 / 192卷 / 06期

关键词：

Schwarz symmetrization; Distribution function; Nonlinear elliptic problem; Eigenvalue problem; Optimal estimates; Degenerate elliptic equation; CONSTANT IMPROVEMENT; COMPARISON-THEOREMS; DEGENERATE; EIGENFUNCTIONS; REARRANGEMENTS; UNIQUENESS;

D O I：

10.1007/s10231-012-0255-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the existence and bound of solutions for some nonlinear equation. Moreover, for some nonlinear problems, we show that if the first p-eigenvalue of a domain is big, the supremum of a solution related to this domain is close to zero. For that we obtain L-infinity estimates for solutions of nonlinear and eigenvalue problems in terms of other L (p) norms.

引用

页码：987 / 1024

页数：38

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