Sobolev space properties of superharmonic functions on metric spaces
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- Kinnunen, J. & Martio, O. Results. Math. (2003) 44: 114. doi:10.1007/BF03322918
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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.