Boundary Value Problems
Volume 2007 (2007), Article ID 48348, 20 pages
doi:10.1155/2007/48348
Unbounded supersolutions of nonlinear equations with nonstandard growth
Petteri Harjulehto1
, Juha Kinnunen2
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
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.