Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient

Abstract

By using Duhamel's formula, we prove sharp two-sided estimates for the heat kernel of spectral fractional Laplacian with time-dependent gradient perturbation in bounded $C^{1,1}$ domains. Moreover, we also obtain gradient estimate as well as Hölder continuity of the gradient of the heat kernel.

References in corpus (1)

• Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains