The Mullins-Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn-Hilliard equation. Assuming the existence of sufficiently smooth solutions we will show that the one-sided Mullins-Sekerka flow does not preserve convexity. The main tool is the strong maximum principle for elliptic second order differential equations.
Electronic J. Diff. Equ., 1993 no. 08, pp. 1-7 (1993)
One-sided Mullins-Sekerka flow does not preserve convexity