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The Martin Kernel for Unbounded Domains

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Abstract

The unbounded domains under consideration include the parabolic-type regions and shrinking one-sided horns that have appeared in the literature. We show the Martin boundary at ∞ is a singleton and we determine the growth of the corresponding Martin kernel. For a parabolic-type region expanding at a power law rate, the growth is subexponential and for a horn shrinking at a power law rate it is superexponential.

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  1. Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX, 77843-3368, USA

    Dante DeBlassie

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  1. Dante DeBlassie
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Correspondence to Dante DeBlassie.

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DeBlassie, D. The Martin Kernel for Unbounded Domains. Potential Anal 32, 389–404 (2010). https://doi.org/10.1007/s11118-009-9156-2

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  • DOI: https://doi.org/10.1007/s11118-009-9156-2

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