A PHASE FIELD MODEL FOR THE OPTIMIZATION OF THE WILLMORE ENERGY IN THE CLASS OF CONNECTED SURFACES

作者：Dondl Patrick W^*; Mugnai Luca; Roeger Matthias

来源：SIAM Journal on Mathematical Analysis, 2014, 46(2): 1610-1632.

DOI：10.1137/130921994

• Willmore energy
• topological constraints
• phase field models
• Gamma-convergence

We consider the problem of minimizing the Willmore energy connected surfaces with prescribed surface area which are confined to a finite container. To this end, we approximate the surface by a phase field function u taking values close to +1 on the inside of the surface and -1 on its outside. The confinement of the surface is now simply given by the domain of definition of u. A diffuse interface approximation for the area functional, as well as for the Willmore energy, are well known. We address the topological constraint of connectedness by a nested minimization of two phase fields, the second one being used to identify connected components of the surface. In this article, we provide a proof of Gamma-convergence of our model to the sharp interface limit.

• 出版日期2014