On the Lipschitz continuity of the heat kernel
Abstract
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 even Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and metric 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.
Fields of Study & Subjects
Optimization and Variational Analysis
Advanced Banach Space Theory
Functional Equations Stability Results
Publication details
- Journal / source
- Journal of Evolution Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 26
- Issue
- 2
- Publication date
- 15 April 2026
- Language
- EN