%0 Journal Article
%T Local solutions to a free boundary problem for the Willmore functional
%A Roberta Alessandroni
%A Ernst Kuwert
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1408.6670v1