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Boundary Value Problems
Boundary Value Problems Cover Image
  • Research Article
  • Open Access

Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

Boundary Value Problems20062007:048348

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

©  Petteri Harjulehto et al. 2007

  • Received: 3 March 2006
  • Accepted: 28 May 2006
  • Published:

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.

Keywords

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

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Authors’ Affiliations

(1)
Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Helsinki, 00014, Finland
(2)
Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, Oulu, 90014, Finland
(3)
Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, Espoo, 02015, Finland

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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.

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