Boundary Value Problems
Volume 2007 (2007), Article ID 48348, 20 pages
Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth
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
Academic Editor: Ugo Pietro Gianazza
Copyright © 2007 Petteri Harjulehto et al. 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.
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.