We consider some free boundary problems involving motion by mean curvature and a nonlocal term. They arise as singular limits of various phase transition models. Using precise regularity estimates in Hölder spaces, we prove that these problems are well-posed. We study the qualitative behavior of the motion law and show in particular that the inclusion of interfaces is not preserved in time.
"Modified motion by mean curvature: local existence and uniqueness and qualitative properties." Differential Integral Equations 13 (10-12) 1371 - 1392, 2000. https://doi.org/10.57262/die/1356061130