Surface diffusion with triple junctions: A stability criterion for stationary solutions
The authors consider a fourth-order geometric flow on a network of curves in a bounded domain \(\Omega\). This flow decreases a weighted total length of the curves and preserves the enclosed volumes. They first formulate the geometric evolution problem as an appropriate PDE problem and give a Poincaré-style estimate on a network of curves. And then, in this paper, the authors study the linearized stability of stationary solutions, using the \(H^{-1}\)-gradient flow structure of the problem, and show that the stationary solutions of this flow are critical points of a partition problem in \(\Omega\).
scientific article; zbMATH DE number 5734997