Boundary Estimates for Certain Degenerate and Singular Parabolic Equations

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.

Cited by in corpus (3)

• Boundary behavior of solutions to the parabolic p-Laplace equation
• A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term
• Existence and stabilization results for a singular parabolic equation involving the fractional Laplacian