Two-sided heat kernel estimates for symmetric diffusion processes with jumps: recent results

DOI10.1007/978-981-19-4672-1_5zbMath1497.60110OpenAlexW4297571831MaRDI QIDQ2088463

Jian Wang, Panki Kim, Zhen-Qing Chen, Takashi Kumagai

Publication date: 22 October 2022

Full work available at URL: https://doi.org/10.1007/978-981-19-4672-1_5

zbMATH Keywords

heat kernel estimateparabolic Harnack inequalityinner uniform domaindiffusion process with jumpssymmetric Dirichlet form

Mathematics Subject Classification ID

Dirichlet forms (31C25) Diffusion processes (60J60) Probabilistic potential theory (60J45) Transition functions, generators and resolvents (60J35) Jump processes on general state spaces (60J76)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global heat kernel estimates for \(\Delta+\Delta^{\alpha/2}\) in half-space-like domains
• Dirichlet forms and symmetric Markov processes.
• Heat kernel upper bounds for symmetric Markov semigroups
• A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps
• Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps
• Upper bounds for symmetric Markov transition functions
• Brownian motion on the Sierpinski gasket
• Renaissance, recollements, mélanges, ralentissement de processus de Markov
• Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms
• On estimates of transition density for subordinate Brownian motions with Gaussian components in \(C^{1,1}\)-open sets
• Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms
• Energy inequalities for cutoff functions and some applications
• Heat kernel estimates for \(\varDelta + \varDelta^{\alpha / 2}\) under gradient perturbation
• Harmonic functions for a class of integro-differential operators
• Heat kernels for non-symmetric diffusion operators with jumps
• Parabolic Harnack inequality for the mixture of Brownian motion and stable process
• Green function estimates and Harnack inequality for subordinate Brownian motions
• Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components
• Heat kernels for reflected diffusions with jumps on inner uniform domains
• Heat kernel estimates for Δ+Δ ^{α /2} in C ^{1, 1} open sets
• Harnack inequality for some discontinuous Markov processes with a diffusion part