Gauge functions, eikonal equations and Bôcher's theorem on stratified Lie groups

DOI10.1007/s00526-006-0087-0zbMath1137.31003OpenAlexW2013115925WikidataQ115387731 ScholiaQ115387731MaRDI QIDQ2642934

Andrea Bonfiglioli, Ermanno Lanconelli

Publication date: 6 September 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-006-0087-0

zbMATH Keywords

fundamental solutionsub-LaplacianCarnot groupstratified Lie groupBôcher type theorem

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Subelliptic equations (35H20)

Related Items (7)

Subharmonic functions in sub-Riemannian settings ⋮ A counterexample to the monotone increasing behavior of an Alt-Caffarelli-Friedman formula in the Heisenberg group ⋮ ``Potato kugel for sub-Laplacians ⋮ Normal families of functions for subelliptic operators and the theorems of Montel and Koebe ⋮ The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE ⋮ Pizzetti's formula for H-type groups ⋮ A Liouville-type Theorem on half-spaces for sub-Laplacians

Cites Work

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• Subelliptic estimates and function spaces on nilpotent Lie groups
• Uniform Gaussian estimates of the fundamental solutions for heat operators on Carnot groups.
• Subharmonic functions on Carnot groups
• Hypoelliptic second order differential equations
• Mean values and differential equations
• Bocher's Theorem
• On the weak continuity of elliptic operators and applications to potential theory
• Liouville-type theorems for real sub-Laplacians
• Surface measures in Carnot-Carathéodory spaces

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