On fractional Leibniz rule for Dirichlet Laplacian in exterior domain
Vladimir S. Georgiev, Koichi Taniguchi · Discrete and Continuous Dynamical Systems · 2018
The goal of the work is to verify the fractional Leibniz rule for Dirichlet Laplacian in the exterior domain of a compact set. The key point is the proof of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem.