6 papers · 1 filter
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…
Inverse Iteration for the Monge-Ampère Eigenvalue Problem
Farhan Abedin, Jun Kitagawa
We present an iterative method based on repeatedly inverting the Monge-Ampère operator with Dirichlet boundary condition and prescribed right-hand side on a bounded, convex domain…
Exponential Convergence of Parabolic Optimal Transport on Bounded Domains
Farhan Abedin, Jun Kitagawa
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Ampère type arising from optimal mass transport. Our main result is…
Harnack's inequality for a class of non-divergent equations in the Heisenberg group
Farhan Abedin, Cristian E. Gutiérrez, Giulio Tralli
We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, c…
estimates for the parallel refractor
Farhan Abedin, Cristian E. Gutierrez, Giulio Tralli
We consider the parallel refractor problem when the planar radiating source lies in a medium having higher refractive index than the medium in which the target is located. We prove…