Time regularity for local weak solutions of the heat equation on local Dirichlet spaces

DOI10.1007/s11118-022-10039-4arXiv1912.12998OpenAlexW2997716900MaRDI QIDQ6188070

Qi Hou, Laurent Saloff-Coste

Publication date: 1 February 2024

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.12998

zbMATH Keywords

heat equationDirichlet form

Mathematics Subject Classification ID

Dirichlet forms (31C25) Heat equation (35K05) Dirichlet form methods in Markov processes (60J46)

Related Items

On the caloric functions with BMO traces and their limiting behaviors ⋮ Rough hypoellipticity for the heat equation in Dirichlet spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Widder's representation theorem for symmetric local Dirichlet spaces
• The heat semigroup and Brownian motion on strip complexes
• Dirichlet forms and symmetric Markov processes.
• Spaces of smooth functions and distributions on infinite-dimensional compact groups
• Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms
• Uniformly elliptic operators on Riemannian manifolds
• Small-time asymptotic estimates in local Dirichlet spaces
• Small time heat kernel behavior on Riemannian complexes
• The Riemannian structure of Alexandrov spaces
• Heat kernel bounds, conservation of probability and the Feller property
• Small-time Gaussian behavior of symmetric diffusion semigroups
• Invariant local Dirichlet forms on locally compact groups
• Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces
• Stability of the elliptic Harnack inequality
• On singularity of energy measures on self-similar sets
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• Optimal bounds for ancient caloric functions
• On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates
• Energy inequalities for cutoff functions and some applications
• On a martingale method for symmetric diffusion processes and its applications
• On some types of topological groups
• Davies’ method for anomalous diffusions
• Hypoelliptic Bi-Invariant Laplacians on Infinite Dimensional Compact Groups
• Non-Gaussian Aspects of Heat Kernel Behaviour
• Elliptic diffusions on infinite products.
• A note on time analyticity for ancient solutions of the heat equation
• On Ancient Solutions of the Heat Equation
• Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem
• Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces