C02 Intrinsic convexity in the Mullins-Sekerka evolution

Intrinsic convexity has been introduced and capitalized on by Otto and M. Westdickenberg to prove contraction estimates for the porous medium equation. The HED method to establish convergence of nonconvex gradient flows has been developed by Otto and M. G. Westdickenberg and exploited in joint work with Chugreeva for the Mullins-Sekerka (MS) evolution. In this project we combine the insights of these previous works to hunt for “optimal convexity” of the MS problem.