8 papers
Parabolic uniform rectifiability is characterized by Carleson measure estimates for bounded caloric functions
Simon Bortz, Pablo Hidalgo-Palencia, Steve Hofmann +1
We show that the parabolic uniform rectifiability of a set can be characterized by an interior PDE property, namely Carleson measure estimates for bounded solutions to the heat equ…
Solvability of the Dirichlet problem for the heat equation implies parabolic uniform rectifiability
Simon Bortz, Steven Hofmann, José María Martell +1
Let be an open set in space-time with boundary . Under minimal and natural background assumptions - namely, that is time-symmetricall…
A Characterization of Solvability of the Parabolic 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- domain obey a Carleson measure estimate, then the…
A Variable Coefficient Free Boundary Problem for -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 Nyström [BHMN25]. In particular, we show that if is the region above the graph of a…
The Dirichlet Problem for elliptic equations with singular drift terms
Steve Hofmann
We establish solvability of the Dirichlet problem, for some finite , in a 1-sided chord-arc domain (i.e., a uniform domain with Ahlfors-David regular boundary), for el…
Parabolic Singular Integrals with Nonhomogeneous Kernels
Simon Bortz, John Hoffman, Steve Hofmann +2
We establish 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…