Solvability of the $L^p$ Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph

Simon Bortz, Steven Hofmann, José María Martell +1

We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is a parabolic $A_{\infty }$ weight with respect to surface measure (w…