Local solutions to a free boundary problem for the Willmore functional

Roberta Alessandroni; Ernst Kuwert

Local solutions to a free boundary problem for the Willmore functional

Differential Geometry 2014-08-29 v1 Analysis of PDEs

Authors: Roberta Alessandroni , Ernst Kuwert

Abstract

We consider a free boundary problem for the Willmore functional. Given a smooth domain $\Omega$ in ${\mathbb R}^3$ , we construct Willmore disks wich are critical in the class of surfaces meeting $\partial \Omega$ orthogonally along their boundary and having small prescribed area. Using rescaling we first obtain constrained solutions with prescribed two-dimensional barycenter, and then study the variation of the barycenter.

Keywords

free boundary problem bounded domains boundary value problems

Cite

@article{arxiv.1408.6670,
  title  = {Local solutions to a free boundary problem for the Willmore functional},
  author = {Roberta Alessandroni and Ernst Kuwert},
  journal= {arXiv preprint arXiv:1408.6670},
  year   = {2014}
}

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