Sobolev space properties of superharmonic functions on metric spaces |
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| Authors: | Juha Kinnunen Olli Martio |
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| Institution: | 1. K., Institute of Mathematics, Helsinki University of Technology, O. Box 1100, N-02015, Finland
2. O.M., Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Finland
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| Abstract: | Our objective is to study regularity of superharmonic functions of a nonlinear potential theory on metric measure spaces. In particular, we are interested in the local integrability properties of a superharmonic function and its derivative. We show that every superharmonic function has a weak upper gradient and provide sharp local integrability estimates. In addition, we study absolute continuity of a superharmonic function. |
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