Boundary regularity for degenerate and singular parabolic equations

  • Anders Björn
  • Jana Björn
  • Ugo Gianazza
  • Mikko Parviainen


We characterise regular boundary points of the parabolic \(p\)-Laplacian in terms of a family of barriers, both when \(p>2\) and \(1<p<2\). By constructing suitable families of such barriers, we give some simple geometric conditions that ensure the regularity of boundary points.

Mathematics Subject Classification (2010)

Primary 35K20 Secondary 31B25 35B65 35K65 35K67 35K92 



A. B. and J. B. are supported by the Swedish Research Council, and M. P. by the Academy of Finland. Part of this research was done during several visits: of M. P. to Linköpings universitet in 2007, of A. B. to Università di Pavia in 2011, of U. G. to University of Jyväskylä in 2012, and while all authors visited Institut Mittag-Leffler in 2013.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Anders Björn
    • 1
  • Jana Björn
    • 1
  • Ugo Gianazza
    • 2
  • Mikko Parviainen
    • 3
  1. 1.Department of MathematicsLinköpings universitetLinköpingSweden
  2. 2.Department of Mathematics “F. Casorati”Università di PaviaPaviaItaly
  3. 3.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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