Boundary estimates for certain degenerate and singular parabolic equations
Benny Avelin, Ugo Gianazza, Sandro Salsa · Journal of the European Mathematical Society · 2016
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic p -Laplacian equation. 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.