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arXiv · 1406.1039

Boundary Estimates for Certain Degenerate and Singular Parabolic Equations

Benny Avelin·Ugo Gianazza·Sandro Salsa
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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 $p$-Laplacian. Assuming that such solutions continuously vanish on some distinguished part of the lateral part $S_T$ 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.

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Benny Avelin, Ugo Gianazza, Sandro Salsa. 2014-06-04. Boundary Estimates for Certain Degenerate and Singular Parabolic Equations. https://doi.org/10.4171/jems%2F593

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