69 citations · 192 across the 31 of their papers we have counts for
35 papers
Slowly vanishing mean oscillations: non-uniqueness of blow-ups in a two-phase free boundary problem
Matthew Badger, Max Engelstein, Tatiana Toro
In Kenig and Toro's two-phase free boundary problem, one studies how the regularity of the Radon-Nikodym derivative of harmonic measures on complementary NTA domains…
Branch Points for (Almost-)Minimizers of Two-Phase Free Boundary Problems
Guy David, Max Engelstein, Mariana Smit Vega Garcia +1
We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt- Caffarelli-Friedman type f…
Łojasiewicz Inequalities and Generic Smoothness of Nodal Sets of Solutions to Elliptic PDE
Matthew Badger, Max Engelstein, Tatiana Toro
In this article, we prove that for a broad class of second order elliptic PDEs, including the Laplacian, the zero sets of solutions to the Dirichlet problem are smooth for "generic…
Elliptic measures for Dahlberg-Kenig-Pipher operators: Asymptotically optimal estimates
Simon Bortz, Tatiana Toro, Zihui Zhao
Questions concerning quantitative and asymptotic properties of the elliptic measure corresponding to a uniformly elliptic divergence form operator have been the focus of recent stu…
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…
Optimal Poisson kernel regularity for elliptic operators with Hölder-continuous coefficients in vanishing chord-arc domains
Simon Bortz, Tatiana Toro, Zihui Zhao
We show that if is a vanishing chord-arc domain and is a divergence-form elliptic operator with Hölder-continuous coefficient matrix, then , where i…