### Surface diffusion with triple junctions: A stability criterion for stationary solutions

#### Abstract

We study a fourth-order geometric evolution problem on a network of curves in a bounded domain $\Omega$. The flow decreases a weighted total length of the curves and preserves the enclosed volumes. Stationary solutions of the flow are critical points of a partition problem in $\Omega$. In this paper we study the linearized stability of stationary solutions using the $H^{-1}$-gradient flow structure of the problem. Important issues are the development of an appropriate PDE formulation of the geometric problem and Poincaré type estimate on a network of curves.

#### Article information

Source
Adv. Differential Equations, Volume 15, Number 5/6 (2010), 437-472.

Dates
First available in Project Euclid: 18 December 2012