7 citations · 7 across the 6 of their papers we have counts for
5 papers · 1 filter
Optimality in nonlocal time-dependent obstacle problems
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
This paper showcases the effectiveness of the quasiconvexity property in addressing the optimal regularity of the temporal derivative and establishes conditions for its continuity…
The Two-Phase Stefan Problem with Anomalous Diffusion
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admi…
On the regularity of the Non-dynamic Parabolic Fractional Obstacle Problem
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
In the class of the so called non-dynamic Fractional Obstacle Problems of parabolic type, it is shown how to obtain higher regularity as well as optimal regularity of the space der…
Parabolic Obstacle Problems. Quasi-convexity and Regularity
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
In a wide class of the so called Obstacle Problems of parabolic type it is shown how to improve the optimal regularity of the solution and as a consequence how to obtain space-time…
The structure of the free boundary for lower dimensional obstacle problems
I. Athanasopoulos, L. A. Caffarelli, S. Salsa
We study the regularity of the "free surface" in boundary obstacle problems. We show that near a non-degenerate point the free boundary is a -dimensional surface i…