Calculus of Variations and Geometric Measure Theory
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A Phase Field Model for Thin Elastic Structures with Topological Constraint

Patrick W. Dondl

created by gelli on 25 Feb 2018
modified on 12 Mar 2018

14 mar 2018 -- 17:00   [open in google calendar]

Sala Seminari (Dipartimento di Matematica di Pisa)


With applications in the area of biological membranes in mind, we consider the problem of minimizing Willmore’s energy among the class of closed, connected surfaces with given surface area that are confined to a fixed container. Based on a phase field model for Willmore’s energy originally introduced by de Giorgi, we develop a technique to incorporate the connectedness constraint into a diffuse interface model of elastic membranes. Our approach uses a geodesic distance function associated to the phase field to discern different connected components of the support of the limiting mass measure. We obtain both a suitable compactness property for finite energy sequences as well as a Gamma-convergence result. Furthermore, we present computational evidence for the effectiveness of our technique. The main argument in our proof is based on a new, natural notion to describe convergence of phase fields.

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