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Register a new userLocal behavior of p-harmonic Greens functions in metric spaces
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We describe the behavior of p-harmonic Greens functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincare inequality.
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We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a $(1,1)$-Poincare inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of [23, 29], solutions by considering the Dirichlet problem for $p$-harmonic functions, $p>1$, and letting $pto 1$. Tools developed and used in this paper include the inner perimeter measure of a domain.
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