101 citations · 841 across the 59 of their papers we have counts for
67 papers
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 María 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…
On the Kato problem for elliptic operators in non-divergence form
Luis Escauriaza, Pablo Hidalgo-Palencia, Steve Hofmann
We consider the Kato square root problem for non-divergence second order elliptic operators , and, especially, the normalized adjoints of such operators. In par…
Critical Perturbations for Second Order Elliptic Operators. Part II: Non-tangential maximal function estimates
Simon Bortz, Steve Hofmann, José Luis Luna Garcia +2
This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators by first and zero order…
Regularity and Neumann problems for operators with real coefficients satisfying Carleson condition
Martin Dindoš, Steve Hofmann, Jill Pipher
In this paper, we continue the study of a class of second order elliptic operators of the form $\mathcal L=\mbox{div}(A\nabla\cdot)$ in a domain above a Lipschitz graph in $\mathbb…
Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets
Simon Bortz, John Hoffman, Steve Hofmann +2
Let be a parabolic uniformly rectifiable set. We prove that every bounded solution to $$\partial_tu- Δu=0, \quad \text{in} \quad \mathbb R^{n+1}\set…
Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition
Murat Akman, Steve Hofmann, José María Martell +1
Let , , be a 1-sided non-tangentially accessible domain (aka uniform domain), that is, satisfies the interior Corkscrew and Harnack chain cond…