19 citations · 20 across the 9 of their papers we have counts for
11 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…
Boundary regularity for subelliptic equations in the Heisenberg group
Farhan Abedin, Giulio Tralli
We prove boundary Hölder and Lipschitz regularity for a class of degenerate elliptic, second order, inhomogeneous equations in non-divergence form structured on the left-invariant…
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…
Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem
Farhan Abedin, William M Feldman
We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of…
A perturbative approach to the parabolic optimal transport problem for non-MTW costs
Farhan Abedin, Jun Kitagawa
Fix a pair of smooth source and target densities and of equal mass, supported on bounded domains . Also fix a cost function $c_0 \in C^{4,α}(…
Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations
Farhan Abedin, Russell W. Schwab
We establish that the regularity theory for translation invariant fractional order parabolic integro-differential equations (via Krylov-Safonov estimates) gives an improv…