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The Fundamental Convergence Theorem for p(·)-Superharmonic Functions

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Abstract

We study the balayage related to the supersolutions of the variable exponent p(·)-Laplace equation. We prove the fundamental convergence theorem for the balayage and apply it for proving the Kellogg property, boundary regularity results for the balayage, and a removability theorem for p(·)-solutions.

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Authors and Affiliations

  1. Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland

    Visa Latvala & Olli Toivanen

  2. Department of Mathematical Sciences, NTNU, 7491, Trondheim, Norway

    Teemu Lukkari

Authors
  1. Visa Latvala
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  2. Teemu Lukkari
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  3. Olli Toivanen
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Correspondence to Visa Latvala.

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Latvala, V., Lukkari, T. & Toivanen, O. The Fundamental Convergence Theorem for p(·)-Superharmonic Functions. Potential Anal 35, 329–351 (2011). https://doi.org/10.1007/s11118-010-9215-8

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  • DOI: https://doi.org/10.1007/s11118-010-9215-8

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