Gradient estimates and their optimality for heat equation in an exterior domain
Analysis of PDEs
2017-10-03 v1
Abstract
This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem. Applications of these estimates to bilinear type commutator estimates for Laplace operator with Dirichlet boundary condition in exterior domain are discussed too.
Keywords
Cite
@article{arxiv.1710.00592,
title = {Gradient estimates and their optimality for heat equation in an exterior domain},
author = {Vladimir Georgiev and Koichi Taniguchi},
journal= {arXiv preprint arXiv:1710.00592},
year = {2017}
}
Comments
15 pages