Steve Hofmann

collaborators

5 papers

math.AP2026

The Dirichlet Problem for elliptic equations with singular drift terms

Steve Hofmann

We establish $L^{p}$ solvability of the Dirichlet problem, for some finite $p$ , in a 1-sided chord-arc domain $I^c ◯$ (i.e., a uniform domain with Ahlfors-David regular boundary), for e…

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.AP2025

A Characterization of Solvability of the Parabolic $L^{p}$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions

James Warta, Steve Hofmann

In this paper, we show that if the bounded solutions to the parabolic Dirichlet problem on a Lipshitz- $[1, \frac{1}{2}]$ domain obey a Carleson measure estimate, then the…

math.CA2025

Parabolic Singular Integrals with Nonhomogeneous Kernels

Simon Bortz, John Hoffman, Steve Hofmann +2

We establish $L^{2}$ boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here is that we include non-h…

math.AP2025

A Variable Coefficient Free Boundary Problem for $L^{p}$ -solvability of Parabolic Dirichlet Problems in Graph Domains

Simon Bortz, Sandra Ferris, Pablo Hidalgo-Palencia +1

We investigate variable coefficient analogs of a recent work of Bortz, Hofmann, Martell and NystrÃ¶m [BHMN25]. In particular, we show that if $I^c ◯$ is the region above the graph of…

The Dirichlet Problem for elliptic equations with singular drift terms

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

A Characterization of Solvability of the Parabolic Lp Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions

Parabolic Singular Integrals with Nonhomogeneous Kernels

A Variable Coefficient Free Boundary Problem for Lp-solvability of Parabolic Dirichlet Problems in Graph Domains

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

A Characterization of Solvability of the Parabolic $L^{p}$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions

A Variable Coefficient Free Boundary Problem for $L^{p}$ -solvability of Parabolic Dirichlet Problems in Graph Domains