J. M. Martell

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20242026

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math.AP2025

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

Simon Bortz, Steven Hofmann, JosÃ© MarÃa Martell +1

Let $I^c ◯ \subset R^{n + 1}$ be an open set in space-time with boundary $I^£ = \partial I^c ◯$ . Under minimal and natural background assumptions - namely, that $I^£$ is time-symmetri…

math.AP2024

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

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…

Solvability of the Lp Dirichlet problem for the heat equation implies parabolic uniform rectifiability

Solvability of the Lp Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph

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

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