Hölder continuity for Trudinger’s equation in measure spaces

  • Tuomo Kuusi
  • Rojbin Laleoglu
  • Juhana Siljander
  • José Miguel Urbano


We complete the study of the regularity for Trudinger’s equation by proving that weak solutions are Hölder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling.

Mathematics Subject Classification (2000)

35B65 35K67 35D10 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Tuomo Kuusi
    • 1
  • Rojbin Laleoglu
    • 2
  • Juhana Siljander
    • 1
  • José Miguel Urbano
    • 2
  1. 1.Institute of MathematicsAalto UniversityAaltoFinland
  2. 2.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal

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