Potential analysis for a class of diffusion equations: a Gaussian bounds approach
type: Item
instance of: scholarly article
title: Potential analysis for a class of diffusion equations: a Gaussian bounds approach
zbMATH Open document ID: 1191.35104
author: Ermanno Lanconelli
author: F. Uguzzoni
published in: Journal of Differential Equations
publication date: 2010-04-13T00:00:00Z
review text: The authors axiomatically develop a potential analysis for a general class of hypoelliptic diffusion equations under the following basic assumptions: doubling condition and segment property for an underlying distance and Gaussian bounds of the fundamental solution. The analysis is principally aimed to obtain regularity criteria and uniform boundary estimates for the Perron-Wiener solution to the Dirichlet problem. As an example of application, the authors also derive an exterior cone criterion of boundary regularity and scale-invariant Harnack inequality and Hölder estimate for an important class of operators in non-divergence form with Hölder continuous coefficients, modeled on Hörmander vector fields.
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 31E05
zbMATH DE Number: 5692556
zbMATH Keywords: non-divergence Hörmander operators
zbMATH Keywords: Harnack inequality
zbMATH Keywords: exterior cone criterion
MaRDI profile type: Publication
full work available at URL: j.jde.2010.01.007
OpenAlex ID: W1919107993
cites work: Bounds for the fundamental solution of a parabolic equation
cites work: Harmonic spaces and their potential theory
cites work: Uniform Gaussian estimates of the fundamental solutions for heat operators on Carnot groups.
cites work: Fundamental solutions for non-divergence form operators on stratified groups
cites work: Harnack inequality for non-divergence form operators on stratified groups
cites work: Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
cites work: Schauder estimates for parabolic nondivergence operators of Hörmander type
cites work: Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities
cites work: On topologies and boundaries in potential theory. Enlarged ed. of a course of lectures delivered in 1966
cites work: Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics
cites work: Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature
cites work: Neuronal Oscillations in the Visual Cortex: $\Gamma$-Convergence to the Riemannian Mumford--Shah Functional
cites work: Q5662251
cites work: Covering theorems, inequalities on metric spaces and applications to PDE's
cites work: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
cites work: Flow of real hypersurfaces by the trace of the Levi form
cites work: Q3771355
cites work: Q3509941
cites work: On the fundamental solution for hypoelliptic second order partial differential equations with non-negative characteristic form
cites work: Q4429188
cites work: Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems
cites work: A tour of subriemannian geometries, their geodesics and applications
cites work: Q3345176
cites work: Aspects of Sobolev-type inequalities
cites work: Opérateurs uniformément sous-elliptiques sur les groupes de Lie. (Uniformly sub-elliptic operators on Lie groups)
cites work: Weak solutions for the Levi equation and envelope of holomorphy
DOI: 10.1016/J.JDE.2010.01.007
description: scientific article; zbMATH DE number 5692556