Local behavior of \(p\)-harmonic Green's functions in metric spaces

DOI10.1007/s11118-009-9154-4zbMath1191.31006arXiv0807.1323OpenAlexW3106027574MaRDI QIDQ964219

Nicola Garofalo, Niko Marola, Donatella Danielli

Publication date: 15 April 2010

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.1323

zbMATH Keywords

Green functionp-Laplace equationp-harmonic functionp-Dirichlet integral

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (11)

Sharp capacity estimates for annuli in weighted \(\mathbf {R}^n\) and in metric spaces ⋮ Existence and almost uniqueness for \(p\)-harmonic Green functions on bounded domains in metric spaces ⋮ Volume growth, capacity estimates, \(p\)-parabolicity and sharp integrability properties of \(p\)-harmonic Green functions ⋮ Hardy-Sobolev type inequalities with sharp constants in Carnot-Carathéodory spaces ⋮ Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces ⋮ Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property ⋮ Wolff potential estimates for Cheeger \(p\)-harmonic functions ⋮ Locally \(p\)-admissible measures on \(\mathbf{R}\) ⋮ Local and semilocal Poincaré inequalities on metric spaces ⋮ Green functions for weighted subelliptic \(p\)-Laplace operator constructed by Hörmander's vector fields ⋮ Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moser iteration for (quasi)minimizers on metric spaces
• Balls and metrics defined by vector fields. I: Basic properties
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Hypoelliptic differential operators and nilpotent groups
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Singular functions on metric measure spaces.
• Sobolev space properties of superharmonic functions on metric spaces
• Lectures on analysis on metric spaces
• Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces
• Definitions of Sobolev classes on metric spaces
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups
• Boundary continuity for quasiminimizers on metric spaces
• Sobolev spaces with zero boundary values on metric spaces
• Local behavior of solutions of quasi-linear equations
• Geometric implications of the Poincaré inequality
• Isolated singularities of solutions of quasi-linear equations
• Sharp capacitary estimates for rings in metric spaces
• A note on the isoperimetric constant
• Removable sets for the poincare inequality on metric spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations
• Regularity of quasi-minimizers on metric spaces
• Harmonic functions on metric spaces

This page was built for publication: Local behavior of \(p\)-harmonic Green's functions in metric spaces