Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

  • Petteri Harjulehto1Email author,

    Affiliated with

    • Juha Kinnunen2 and

      Affiliated with

      • Teemu Lukkari3

        Affiliated with

        Boundary Value Problems20062007:048348

        DOI: 10.1155/2007/48348

        Received: 3 March 2006

        Accepted: 28 May 2006

        Published: 30 October 2006

        Abstract

        We show that every weak supersolution of a variable exponent http://static-content.springer.com/image/art%3A10.1155%2F2007%2F48348/MediaObjects/13661_2006_Article_650_IEq1_HTML.gif -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’ Affiliations

        (1)
        Department of Mathematics and Statistics, University of Helsinki
        (2)
        Department of Mathematical Sciences, University of Oulu
        (3)
        Institute of Mathematics, Helsinki University of Technology

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        Copyright

        © Petteri Harjulehto et al. 2007

        This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.