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Boundary Value Problems
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Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

Boundary Value Problems volume 2007, Article number: 048348 (2006) | Download Citation

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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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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

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Correspondence to Petteri Harjulehto.

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Keywords

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