Schröodinger equations and heat kernel upper bounds on metric spaces

DOI10.1515/FORUM.2010.064zbMath1213.47050OpenAlexW1978993328MaRDI QIDQ3060235

Jiaxin Hu, Martina Zähle

Publication date: 1 December 2010

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum.2010.064

zbMATH Keywords

Dirichlet formsheat kernelsmetric measure spaceoff-diagonal upper bounds

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Schrödinger equations defined by a class of self-similar measures

Cites Work

• Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces
• Hardy-Littlewood theory for semigroups
• Brownian motion on the Sierpinski gasket
• Harmonic analysis for resistance forms.
• Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
• Ultracontractivity and Nash type inequalities
• Sub-Gaussian estimates of heat kernels on infinite graphs
• Functional inequalities for empty essential spectrum
• Heat kernel estimates on effective resistance metric spaces
• Comparison Theorems on Dirichlet Norms and their Applications
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Local Nash Inequality and Inhomogeneity of Heat Kernels
• Sobolev inequalities in disguise