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Open Access Research Article

Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

Petteri Harjulehto1*, Juha Kinnunen2 and Teemu Lukkari3

Author 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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Boundary Value Problems 2007, 2007:048348  doi:10.1155/2007/48348

Published: 30 October 2006

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.