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Asymptotic Behavior of Positive Harmonic Functions in Certain Unbounded Domains

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Abstract

We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g., various paraboloids and horns.

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Authors and Affiliations

  1. Purdue University, 150 N. University Street, West Lafayette, IN, 47907, USA

    Koushik Ramachandran

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  1. Koushik Ramachandran
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Correspondence to Koushik Ramachandran.

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The author was partially supported by the NSF grant DMS - 1067886.

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Ramachandran, K. Asymptotic Behavior of Positive Harmonic Functions in Certain Unbounded Domains. Potential Anal 41, 383–405 (2014). https://doi.org/10.1007/s11118-013-9374-5

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  • DOI: https://doi.org/10.1007/s11118-013-9374-5

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