arXiv:1710.00592 Abstract | arXiv Analytics

arXiv:1710.00592 [math.AP]Abstract References Reviews Resources

Gradient estimates and their optimality for heat equation in an exterior domain

Published 2017-10-02Version 1

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.

Comments: 15 pages

Categories: math.AP

Subjects: 35K05, 35K20

Keywords: exterior domain, heat equation, gradient estimates, dirichlet problem, optimality

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