Heat Kernels in Sub-Riemannian Settings

DOI10.1007/978-3-642-01674-5_2zbMath1196.35116OpenAlexW157698280MaRDI QIDQ3653068

Ermanno Lanconelli

Publication date: 18 December 2009

Published in: Geometric Analysis and PDEs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-01674-5_2

zbMATH Keywords

Harnack inequalitiesCarnot-Carathéodory metricsmotion by Levi curvatures

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Hypoelliptic equations (35H10) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Second-order parabolic equations (35K10)

Cites Work

• Opérateurs uniformément sous-elliptiques sur les groupes de Lie. (Uniformly sub-elliptic operators on Lie groups)
• Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator
• Potential analysis for a class of diffusion equations: a Gaussian bounds approach
• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Analysis on nilpotent groups
• Weak solutions for the Levi equation and envelope of holomorphy
• Hypoelliptic differential operators and nilpotent groups
• Geometric properties of solutions of the Levi-equation
• Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems
• Continuity of Solutions of Parabolic and Elliptic Equations
• Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
• Regularity for quasilinear second‐order subelliptic equations
• REAL HYPERSURFACES EVOLVING BY LEVI CURVATURE: SMOOTH REGULARITY OF SOLUTIONS TO THE PARABOLIC LEVI EQUATION
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