JournalsjemsVol. 18, No. 2pp. 381–424

Boundary estimates for certain degenerate and singular parabolic equations

  • Benny Avelin

    Uppsala Universitet, Sweden
  • Ugo Gianazza

    Università di Pavia, Italy
  • Sandro Salsa

    Politecnico di Milano, Italy
Boundary estimates for certain degenerate and singular parabolic equations cover
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Abstract

We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic pp-Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part STS_T of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular parabolic equations of porous medium type.

Cite this article

Benny Avelin, Ugo Gianazza, Sandro Salsa, Boundary estimates for certain degenerate and singular parabolic equations. J. Eur. Math. Soc. 18 (2016), no. 2, pp. 381–424

DOI 10.4171/JEMS/593