This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

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

The electronic version of this article is the complete one and can be found online at:

Received:3 March 2006
Revisions received:16 May 2006
Accepted:28 May 2006
Published:30 October 2006

© 2007 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.


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