Boundary Value Problems 
Volume 2007 (2007), Article ID 48348, 20 pages
doi:10.1155/2007/48348
Research Article

Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

Petteri Harjulehto,1 Juha Kinnunen,2 and Teemu Lukkari3

 1Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland
2Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014, Oulu, Finland
3Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015, Espoo, Finland
Received 3 March 2006; Revised 16 May 2006; Accepted 28 May 2006

Recommended by Ugo Pietro Gianazza

Abstract

We show that every weak supersolution of a variable exponent p-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.