J. M. Martell

activity

20242026

collaborators

3 papers

math.CA2026

Characterizations of Lyapunov domains in terms of Riesz transforms and the Plemelj-Privalov theorem

Juan JosÃ© MarÃn, JosÃ© MarÃa Martell, Dorina Mitrea +1

We prove several characterizations of $C^{1, I ¨ }$ -domains (aka Lyapunov domains), where $I ¨ $ is a growth function satisfying natural assumptions. For example, given an Ahl…

math.AP2025

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

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…

Characterizations of Lyapunov domains in terms of Riesz transforms and the Plemelj-Privalov theorem

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