Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth
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
Boundary Value Problems 2007, 2007:048348 doi:10.1155/2007/48348Published: 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.