Boundary Estimates for Certain Degenerate and Singular Parabolic Equations
Analysis of PDEs
2016-03-03 v1
Abstract
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic -Laplacian. 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
@article{arxiv.1406.1039,
title = {Boundary Estimates for Certain Degenerate and Singular Parabolic Equations},
author = {Benny Avelin and Ugo Gianazza and Sandro Salsa},
journal= {arXiv preprint arXiv:1406.1039},
year = {2016}
}