Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

TL;DR

This paper provides precise estimates for the heat kernel associated with the fractional Laplacian under Dirichlet boundary conditions across various domain types, including Lipschitz domains.

Contribution

It offers sharp heat kernel estimates for the fractional Laplacian with Dirichlet conditions on general domains, extending previous results to broader classes.

Findings

Sharp heat kernel bounds for fractional Laplacian with Dirichlet conditions

Results applicable to Lipschitz and general domains

Enhanced understanding of boundary behavior of heat kernels

Abstract

We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.