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math.AP2026
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…
math.AP2006
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…