3 papers
math.AP2025
On the asymptotic properties of solutions to one-phase free boundary problems
Max Engelstein, Daniel Restrepo, Zihui Zhao
In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an i…
math.AP2025
On the Grad-Mercier equation and Semilinear Free Boundary Problems
Luis Caffarelli, Antonio Farah, Daniel Restrepo
In this paper, we establish regularity and uniqueness results for Grad-Mercier type equations that arise in the context of plasma physics. We show that solutions of this problem na…
math.AP2024
regularity in semilinear free boundary problems
Daniel Restrepo, Xavier Ros-Oton
We study the higher regularity of solutions and free boundaries in the Alt-Phillips problem , with . Our main results imply that, once free boundaries are $C…