Work

Condenser capacities and capacitary potentials for unbounded sets, and global p -harmonic Green functions on metric spaces

Year: 2024

Type: article

Abstract: We study the condenser capacity capp⁡(E, Ω) on unbounded open sets Ω in a proper connected metric space X equipped with a locally doubling measure supporting a local p-Poincaré inequality, where 1 p is countably subadditive and that it is a Choquet capacity. We next obtain formulas for the capacity of superlevel sets for the capacitary potential. These are then used to show that p-harmonic Green functions exist in an unbounded domain Ω if and only if either X is p-hyperbolic or the Sobolev capacity Cp(X∖Ω)>0. As an application, we deduce new results for Perron solutions and boundary regularity for the Dirichlet boundary value problem for p-harmonic functions in unbounded open sets.

Source: Communications in Partial Differential Equations

DOI: 10.1080/03605302.2024.2411521

Authors: Anders Björn, Jana Björn

Institution: Linköping University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Vetenskapsrådet

Awards: Geometric analysis on Gromov hyperbolic spaces, their boundaries and other metric measure spaces, with applications to p-harmonic functions, Interplay between geometry and analysis on metric spaces and fractal sets, Nonlocal problems and fractional function spaces on metric spaces via hyperbolic fillings, G8660947557