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.
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页码：429 / 469
页数：41
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