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arXiv · 2310.05702

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

Anders Björn·Jana Björn
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Abstract

We study the condenser capacity $\mathrm{cap}_p(E,\Omega)$ on \emph{unbounded} open sets $\Omega$ in a proper connected metric space $X$ equipped with a locally doubling measure supporting a local $p$-Poincar\'e inequality, where $1 0$. 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.

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Anders Björn, Jana Björn. 2023-10-09. Condenser capacities and capacitary potentials for unbounded sets, and global $p$-harmonic Green functions on metric spaces. https://doi.org/10.1080/03605302.2024.2411521

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