Two-sided estimates of heat kernels on metric measure spaces
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Publication:428149
DOI10.1214/11-AOP645zbMath1252.35148arXiv1205.5627OpenAlexW3099116722MaRDI QIDQ428149
Andras Telcs, Alexander Grigor'yan
Publication date: 19 June 2012
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1205.5627
Markov semigroups and applications to diffusion processes (47D07) Fractals (28A80) Heat kernel (35K08)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The construction of Brownian motion on the Sierpinski carpet
- Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds
- Comparison inequalities for heat semigroups and heat kernels on metric measure spaces
- Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces
- Uniqueness of Brownian motion on Sierpiński carpets
- Heat kernel on manifolds with ends
- On the parabolic kernel of the Schrödinger operator
- Brownian motion on the Sierpinski gasket
- A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
- Transition densities for Brownian motion on the Sierpinski carpet
- Dirichlet forms on fractals: Poincaré constant and resistance
- Random walks on graphs with regular volume growth
- Estimates of transition densities for Brownian motion of nested fractals
- Heat kernel upper bounds on a complete non-compact manifold
- Dirichlet forms and symmetric Markov processes
- Transition density estimates for Brownian motion on affine nested fractals
- Transition density estimates for Brownian motion on scale irregular Sierpiński gaskets
- Sub-Gaussian estimates of heat kernels on infinite graphs
- Harnack inequalities and sub-Gaussian estimates for random walks
- On the equivalence of parabolic Harnack inequalities and heat kernel estimates
- The art of random walks.
- Stability of parabolic Harnack inequalities on metric measure spaces
- Resistance forms, quasisymmetric maps and heat kernel estimates
- The Ubiquitous Heat Kernel
- Heat kernel upper bounds for jump processes and the first exit time
- Non-local Dirichlet forms and symmetric jump processes
- Volume doubling measures and heat kernel estimates on self-similar sets
- ON UNIFORM STABILIZATION OF THE SOLUTION OF THE SECOND MIXED PROBLEM FOR A SECOND ORDER PARABOLIC EQUATION
- On Harnack's theorem for elliptic differential equations
- Harmonic Calculus on P.C.F. Self-Similar Sets
- DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY
- Brownian Motion and Harmonic Analysis on Sierpinski Carpets
- Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
- Heat kernels on metric measure spaces and an application to semilinear elliptic equations
- Local Nash Inequality and Inhomogeneity of Heat Kernels
- A harnack inequality for parabolic differential equations
- On the relation between elliptic and parabolic Harnack inequalities
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