Potential analysis for a class of diffusion equations: a Gaussian bounds approach

DOI10.1016/j.jde.2010.01.007zbMath1191.35104OpenAlexW1919107993MaRDI QIDQ963717

Ermanno Lanconelli, Francesco Uguzzoni

Publication date: 13 April 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2010.01.007

zbMATH Keywords

Harnack inequalitynon-divergence Hörmander operatorsexterior cone criterion

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Hypoelliptic equations (35H10) Potential theory on fractals and metric spaces (31E05)

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Cites Work

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• Opérateurs uniformément sous-elliptiques sur les groupes de Lie. (Uniformly sub-elliptic operators on Lie groups)
• Schauder estimates for parabolic nondivergence operators of Hörmander type
• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• Weak solutions for the Levi equation and envelope of holomorphy
• Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics
• Uniform Gaussian estimates of the fundamental solutions for heat operators on Carnot groups.
• Flow of real hypersurfaces by the trace of the Levi form
• On the fundamental solution for hypoelliptic second order partial differential equations with non-negative characteristic form
• Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature
• Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems
• Covering theorems, inequalities on metric spaces and applications to PDE's
• Harmonic spaces and their potential theory
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• On topologies and boundaries in potential theory. Enlarged ed. of a course of lectures delivered in 1966
• Harnack inequality for non-divergence form operators on stratified groups
• Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities
• Neuronal Oscillations in the Visual Cortex: $\Gamma$-Convergence to the Riemannian Mumford--Shah Functional
• Fundamental solutions for non-divergence form operators on stratified groups
• Bounds for the fundamental solution of a parabolic equation