On the Lipschitz continuity of the heat kernel

2023/07/17 by Bifulco, Patrizio, Mugnolo, Delio
#35K90 #47B34 #47D06 #47G10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.08889

Abstract

We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for Hölder or Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and quantum graphs, to Laplacians on a class of fractals including the Sierpiński gasket, and to structurally damped wave equations. An extension to non-autonomous problems is also discussed.

Related

• Properties of Lipschitz smoothing heat semigroups
• Heat kernels and regularity for rough metrics on smooth manifolds
• Functional calculus of operators with heat kernel bounds on non-doubling manifolds with ends
• Discrete Hölder spaces, their characterization via semigroups associated to the discrete Laplacian and kernels estimates
• Hölder regularity of harmonic functions on metric measure spaces