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The p-Harmonic Measure of Small Axially Symmetric Sets

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Abstract

Using the first eigenvalue/eigenvector pair of a singular eigenvalue problem (motivated by the Dirichlet eigenvalue problem for the Laplace-Beltrami operator on a spherical cap), we define certain nonnegative p-superharmonic and p-subharmonic functions on a convex cone which are singular at the vertex and vanish on the rest of the boundary. We use these functions to give upper and lower estimates of the p-harmonic measure near the vertex of the cone as well as the p-harmonic measure of a small spherical cap.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, P. O. Box 30001, Department 3MB, Las Cruces, NM, 88003-8001, USA

    Dante DeBlassie & Robert G. Smits

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  1. Dante DeBlassie
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  2. Robert G. Smits
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Correspondence to Dante DeBlassie.

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DeBlassie, D., Smits, R.G. The p-Harmonic Measure of Small Axially Symmetric Sets. Potential Anal 49, 583–608 (2018). https://doi.org/10.1007/s11118-017-9668-0

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  • DOI: https://doi.org/10.1007/s11118-017-9668-0

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