27 citations · 31 across the 6 of their papers we have counts for
8 papers
A fully nonlinear parabolic segregation problem
Emily Casey, Cornelia Mihaila, María Soria-Carro +1
We study a two-phase parabolic free boundary problem arising as the segregation limit of a competition-diffusion system with strong interactions and fully nonlinear diffusion. The…
An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
Dennis Kriventsov, María Soria-Carro
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating…
Fully nonlinear parabolic fixed transmission problems
David Jesus, María Soria-Carro
We consider transmission problems for parabolic equations governed by distinct fully nonlinear operators on each side of a time-dependent interface. We prove that if the interface…
Lipschitz regularity for Poisson equations involving measures supported on interfaces
Iñigo U. Erneta, María Soria-Carro
We prove optimal Lipschitz regularity of solutions to Poisson's equation with measure data supported on a interface and with …
A parabolic free transmission problem: flat free boundaries are smooth
Dennis Kriventsov, María Soria-Carro
We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat…
Regularity of viscosity solutions to fully nonlinear elliptic transmission problems
M. Soria-Carro, P. R. Stinga
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory o…
On a family of fully nonlinear integro-differential operators: From fractional Laplacian to nonlocal Monge-Ampère
Luis A. Caffarelli, María Soria-Carro
We introduce a new family of intermediate operators between the fractional Laplacian and the Caffarelli-Silvestre nonlocal Monge-Ampère that are given by infimums of integro-differ…
Regularity for interface transmission problems
L. A. Caffarelli, M. Soria-Carro, P. R. Stinga
We study existence, uniqueness, and optimal regularity of solutions to transmission problems for harmonic functions with interfaces. For this, we develop a novel geometri…