4 papers
Variational properties of Perron's extremal solutions in the Bernoulli one-phase problem
Farhan Abedin, William M. Feldman, Kerrek Stinson
We study the Perron extremal solutions of the stationary one-phase Bernoulli problem. These solutions are important in several applications, but not much is known about the regular…
Regularity of two-phase free boundary minimizers in periodic media
Farhan Abedin, William M Feldman
We study the regularity of minimizers of a two-phase energy functional in periodic media. Our main result is a large scale Lipschitz estimate. We also establish improvement-of-flat…
On convex comparison for exterior Bernoulli problems with discontinuous anisotropy
William M Feldman, Norbert Pozar
We give a new proof of a convex comparison principle for exterior Bernoulli free boundary problems with discontinuous anisotropy.
Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers
William M Feldman
We apply new results on free boundary regularity of one-phase almost minimizers in periodic media to obtain a quantitative convergence rate for the shape optimizers of the first Di…