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math.AP2022
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…
math.AP2021
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…
math.AP2018
Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data
Matthew Badger, Max Engelstein, Tatiana Toro
In non-variational two-phase free boundary problems for harmonic measure, we examine how the relationship between the interior and exterior harmonic measures of a domain $Ω\subset…