Solvability of the $L^p$ Dirichlet problem for the heat equation implies parabolic uniform rectifiability

Simon Bortz, Steven Hofmann, José María Martell +1

Let $\Omega \subset {\mathbb{R}}^{n+1}$ be an open set in space-time with boundary $\Sigma =\partial \Omega$. Under minimal and natural background assumptions - namely, that $\Sigma$ is time-symmetricall…