showing 2 related works from this author
Boundary Regularity for the Porous Medium Equation
2018
We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general -- not necessarily cylindrical -- domains in ${\bf R}^{n+1}$. One of our fundamental tools is a new strict comparison principle between sub- and superpara…
Boundary regularity for degenerate and singular parabolic equations
2013
We characterise regular boundary points of the parabolic $p$-Laplacian in terms of a family of barriers, both when $p>2$ and $1<p<2$. Due to the fact that $p\not=2$, it turns out that one can multiply the $p$-Laplace operator by a positive constant, without affecting the regularity of a boundary point. By constructing suitable families of barriers, we give some simple geometric conditions that ensure the regularity of boundary points.