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Boundary regularity for degenerate and singular parabolic equations

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Abstract

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.

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Notes

  1. We thank P. Lindqvist for bringing this problem to our attention.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematics, Linköpings universitet, 58183 , Linköping, Sweden

    Anders Björn & Jana Björn

  2. Department of Mathematics “F. Casorati”, Università di Pavia, via Ferrata 1, 27100 , Pavia, Italy

    Ugo Gianazza

  3. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014 , Jyväskylä, Finland

    Mikko Parviainen

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  1. Anders Björn
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  2. Jana Björn
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  3. Ugo Gianazza
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Correspondence to Ugo Gianazza.

Additional information

Communicated by Y. Giga.

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Björn, A., Björn, J., Gianazza, U. et al. Boundary regularity for degenerate and singular parabolic equations. Calc. Var. 52, 797–827 (2015). https://doi.org/10.1007/s00526-014-0734-9

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  • DOI: https://doi.org/10.1007/s00526-014-0734-9

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