Discrete versions of the Li-Yau gradient estimate
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Publication:5161595
DOI10.2422/2036-2145.201807_005zbMath1476.35289arXiv1701.04807OpenAlexW3127515006MaRDI QIDQ5161595
Rico Zacher, Moritz Kassmann, Dominik Dier
Publication date: 1 November 2021
Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.04807
Heat equation (35K05) Planar graphs; geometric and topological aspects of graph theory (05C10) A priori estimates in context of PDEs (35B45) Second-order parabolic equations (35K10) Random walks on graphs (05C81) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
Related Items (10)
A gradient estimate on graphs with the \(\mathrm{CDE}(m,K)\)-condition ⋮ Aronson-Bénilan and Harnack estimates for the discrete porous medium equation ⋮ \(\psi\)-Li-Yau inequality for the \(p\)-Laplacian on weighted graphs with the \(CD_p^\psi (m, 0)\) curvature ⋮ Sharp Li-Yau inequalities for Dunkl harmonic oscillators ⋮ Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel ⋮ Long-time behavior of non-local in time Fokker–Planck equations via the entropy method ⋮ Curvature-dimension inequalities for non-local operators in the discrete setting ⋮ The entropy method under curvature-dimension conditions in the spirit of Bakry-Émery in the discrete setting of Markov chains ⋮ A Spacial Gradient Estimate for Solutions to the Heat Equation on Graphs ⋮ Bakry-Émery curvature on graphs as an eigenvalue problem
Cites Work
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- Geodesic convexity of the relative entropy in reversible Markov chains
- Remarks on curvature dimension conditions on graphs
- Logarithmic Harnack inequalities
- Gradient flows of the entropy for finite Markov chains
- Ricci curvature of Markov chains on metric spaces
- Mass transportation and rough curvature bounds for discrete spaces
- On the parabolic kernel of the Schrödinger operator
- Li-Yau inequality on finite graphs via non-linear curvature dimension conditions
- A global Poincaré inequality on graphs via a conical curvature-dimension condition
- Ricci curvature of finite Markov chains via convexity of the entropy
- Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs
- Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs
- Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
- Ricci curvature and eigenvalue estimate on locally finite graphs
- Li-Yau inequality on graphs
- Discrete Curvature and Abelian Groups
- Bakry–Émery Curvature Functions on Graphs
- A weak Harnack inequality for fractional evolution equations with discontinuous coefficients
- Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models
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