On Stable Solutions of Boundary Reaction-Diffusion Equations and Applications to Nonlocal Problems with Neumann Data

被引：0

作者：

Dipierro, Serena ^{[1
]}

Soave, Nicola ^{[2
]}

Valdinoci, Enrico ^{[1
,3
]}

机构：

[1] Univ Milan, Dipartimento Matemat, Via Cesare Saldini 50, I-20133 Milan, Italy

[2] Politecn Milan, Dipartimento Matemat, Via Edoardo Bonardi 9, I-20133 Milan, Italy

[3] Univ Melbourne, Sch Math & Stat, 813 Swanston St, Melbourne, Vic 3010, Australia

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2018年 / 67卷 / 01期

关键词：

Stability; symmetry results; classification of solution; reaction-diffusion equations; nonlocal equations; FRACTIONAL DIFFUSION; NONLINEAR EQUATIONS; LAPLACIAN; INEQUALITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincare-type inequality and classification results for stable solutions, and we apply them to the study of an associated nonlocal problem. We also establish a counterexample in the corresponding framework for the fractional Laplacian.

引用

页码：429 / 469

页数：41

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