Open Access

Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

Boundary Value Problems20062007:048348

DOI: 10.1155/2007/48348

Received: 3 March 2006

Accepted: 28 May 2006

Published: 30 October 2006


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.


Authors’ Affiliations

Department of Mathematics and Statistics, University of Helsinki
Department of Mathematical Sciences, University of Oulu
Institute of Mathematics, Helsinki University of Technology


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© Petteri Harjulehto et al. 2007

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