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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Kinnunen, J., Martio, O. Sobolev space properties of superharmonic functions on metric spaces. Results. Math. 44, 114–129 (2003). https://doi.org/10.1007/BF03322918
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DOI: https://doi.org/10.1007/BF03322918