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Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

Boundary Value Problems volume 2007, Article number: 048348 (2006) Cite this article

Abstract

We show that every weak supersolution of a variable exponent-Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Hölder continuous. As a technical tool we derive Harnack-type estimates for possibly unbounded supersolutions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Helsinki, 00014, Finland

    Petteri Harjulehto

  2. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, Oulu, 90014, Finland

    Juha Kinnunen

  3. Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, Espoo, 02015, Finland

    Teemu Lukkari

Authors
  1. Petteri Harjulehto
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  2. Juha Kinnunen
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  3. Teemu Lukkari
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Correspondence to Petteri Harjulehto.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Harjulehto, P., Kinnunen, J. & Lukkari, T. Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth. Bound Value Probl 2007, 048348 (2006). https://doi.org/10.1155/2007/48348

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  • DOI: https://doi.org/10.1155/2007/48348

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Nonlinear Equation