5 papers · 1 filter
The parabolic Dini- condition and absolute continuity of surface and caloric measure
Simon Bortz, Moritz Egert, Sandra Ferris +1
We show if is the graph of a parabolic Lipschitz function, then parabolic surface measure of is absolutely continuous with respect to its caloric meas…
Solvability of the Dirichlet problem for the heat equation implies parabolic uniform rectifiability
Simon Bortz, Steven Hofmann, José MarÃa Martell +1
Let be an open set in space-time with boundary . Under minimal and natural background assumptions - namely, that is time-symmetri…
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 stability result for parabolic measures of operators with singular drifts
Simon Bortz, Moritz Egert, Olli Saari
We study the operator \[ \partial_t - \text{div} A \nabla + B \cdot \nabla \] in parabolic upper-half-space, where is an elliptic matrix satisfying an oscillation condition and…
Solvability of the 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 MarÃa 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 weight with respect to surface measure (w…