Calculus of Variations and Geometric Measure Theory

E. Acerbi - N. Fusco - V. Julin - M. Morini

Nonlinear stability results for the modified Mullins-Sekerka and the surface diffusion flow

created by morini on 14 Jun 2016
modified by acerbi on 11 Apr 2024


Published Paper

Inserted: 14 jun 2016
Last Updated: 11 apr 2024

Journal: Journal of Differential Geometry
Volume: 113
Pages: 1--53
Year: 2019


It is shown that any three-dimensional periodic configuration that is strictly stable for the area functional is exponentially stable for the surface diffusion flow and for the Mullins-Sekerka or Hele-Shaw flow. The same result holds for three-dimensional periodic configurations that are strictly stable with respect to the sharp-interface Ohta-Kawaski en- ergy. In this case, they are exponentially stable for the so-called modified Mullins-Sekerka flow.