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.
MSC Codes 35K05 (Primary), 35K20 (Secondary)
|Publication status||Published - 2017 Oct 2|
- Dirichlet problem
- Exterior domains
- Gradient estimates
- Heat equations
ASJC Scopus subject areas