Results in Mathematics

, Volume 44, Issue 1, pp 114–129

Sobolev space properties of superharmonic functions on metric spaces


DOI: 10.1007/BF03322918

Cite this article as:
Kinnunen, J. & Martio, O. Results. Math. (2003) 44: 114. doi:10.1007/BF03322918


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.

2000 Mathematics Subject Classification

31C45 46E35 

Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.K., Institute of MathematicsHelsinki University of TechnologyFinland
  2. 2.O.M., Department of MathematicsUniversity of HelsinkiFinland

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