9 papers
Big Pieces of Regular Parabolic (bi-)Lipschitz Images is Equivalent to Parabolic Uniform Rectifiability
Simon Bortz, Matthew Hyde, Mason Sharp
We define the notion of regular parabolic (bi-)Lipschitz images as the parabolic (bi-)Lipschitz maps from -dimensional space time which, up to translation, fix the variable…
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…
Weighted Bounded Variation Revisited
Simon Bortz, Matthew Gossett, Joseph Kasel +1
In this article, we investigate the theory of weighted functions of bounded variation (BV), as introduced by Baldi [Ba01]. Depending on the theorem, we impose lower semicontinuity…
Weighted Sobolev Inequalities via the Meyers--Ziemer Framework: Measures, Isoperimetric Inequalities, and Endpoint Estimates
Simon Bortz, Kabe Moen, Andrea Olivo +2
We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This re…
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…
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…