A Phase Field Model for the Optimization of the Willmore Energy in the Class of Connected Surfaces
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...
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| Veröffentlicht in: | SIAM journal on mathematical analysis 2014-01, Vol.46 (2), p.1610-1632 |
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| container_title | SIAM journal on mathematical analysis |
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| creator | Dondl, Patrick W Mugnai, Luca Roger, Matthias |
| description | 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. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/130921994 |
| format | Article |
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| language | eng |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Approximation Confinement Energy Mathematical analysis Mathematical models Minimization Optimization Surface area Topology |
| title | A Phase Field Model for the Optimization of the Willmore Energy in the Class of Connected Surfaces |
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