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Nonlinear parabolic capacity and polar sets of superparabolic functions |
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| Authors: | Juha Kinnunen Riikka Korte Tuomo Kuusi Mikko Parviainen |
| Institution: | 1. Department of Mathematics, Aalto University, P. O. Box 11100, 00076, Aalto, Finland 2. Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, 00014, Helsinki, Finland 3. Department of Mathematics and Statistics, University of Jyv?skyl?, P. O. Box 35, 40014, Jyv?skyl?, Finland |
| Abstract: | We extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the $p$ -Laplacian type. We study definitions and properties of the nonlinear parabolic capacity and show that the capacity of a compact set can be represented via a capacitary potential. As an application, we show that polar sets of superparabolic functions are of zero capacity. The main technical tools used include estimates for equations with measure data and obstacle problems. |
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