The peak of the solution of elliptic equations
Analysis of PDEs
2016-08-19 v4
Abstract
A counter example of inheritance of convexity of domain of positive solution of Dirichlet boundary value problem and the hot spot problem that proposed by J. Rauch is given. The difficulty of these two problems is that the critical points of the solutions is not singleton but a level curve. However, using Pohozeav identity locally, partial answer to both problems can be derived.
Keywords
Cite
@article{arxiv.1511.04644,
title = {The peak of the solution of elliptic equations},
author = {Janpou Nee},
journal= {arXiv preprint arXiv:1511.04644},
year = {2016}
}
Comments
10 pages, 1 figures