We consider a strongly local (p-homogeneous) Riemannian Dirichlet form, according to the definition by Biroli - Vernole. We introduce the Kato class of Radon measures related to such forms and the corresponding relaxed Dirichlet problems with measures in the Kato class. We establish a Wiener criterion in the interior for the local solutions of the relaxed Dirichlet problem: an interior point is regular iff it is a Wiener point.
Wiener criterion for relaxed Dirichlet problem relative to Riemannian $p$-homogeneous Dirichlet forms
BIROLI, MARCO;DAL FABBRO, FLORANGELA;
2008-01-01
Abstract
We consider a strongly local (p-homogeneous) Riemannian Dirichlet form, according to the definition by Biroli - Vernole. We introduce the Kato class of Radon measures related to such forms and the corresponding relaxed Dirichlet problems with measures in the Kato class. We establish a Wiener criterion in the interior for the local solutions of the relaxed Dirichlet problem: an interior point is regular iff it is a Wiener point.File in questo prodotto:
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