Boundary estimates for certain degenerate and singular parabolic equations
Benny Avelin
Uppsala Universitet, SwedenUgo Gianazza
Università di Pavia, ItalySandro Salsa
Politecnico di Milano, Italy
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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 -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part 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