Calculus of Variations and Geometric Measure Theory

S. Della Corte - A. Diana - C. Mantegazza

Global Existence and Stability for the Modified Mullins-Sekerka and Surface Diffusion Flow

created by root on 26 Jul 2021
modified on 23 Jan 2022


Published Paper

Inserted: 26 jul 2021
Last Updated: 23 jan 2022

Journal: Math. Engineering
Volume: 4
Number: 6
Pages: Paper n.054, 104 pp.
Year: 2022


In this survey we present the state of the art about the asymptotic behavior and stability of the modified Mullins–Sekerka flow and the surface diffusion flow of smooth sets, mainly due to E. Acerbi, N. Fusco, V. Julin and M. Morini. After discussing in detail the properties of the nonlocal Area functional under a volume constraint, of which the two flows are the gradient flow with respect to suitable norms, we show that, in dimensions two and three, for initial sets sufficiently “close” to a smooth strictly stable critical set E for such functional, both flows exist for all positive times and asymptotically “converge” to a translate of E.