# Confined Willmore energy and the Area functional

created by pozzetta on 19 Oct 2017
modified by pozzetta1 on 17 Oct 2018

[BibTeX]

Preprint

Inserted: 19 oct 2017
Last Updated: 17 oct 2018

Year: 2018

Abstract:

We consider minimization problems of functionals given by the diﬀerence between the Willmore functional of a surface and its area, when the latter multiplied by a positive constant weight $\Lambda$ and when the surfaces are conﬁned in a bounded open set $\Omega\subset\mathbb{R}^3$. We give a description of the value of the inﬁma and of the convergence of minimising sequences to integer rectiﬁable varifolds in function of the parameter $\Lambda$. We also analyse some properties of these functionals and we provide some examples. Finally we prove the existence of a $C^{1,α}\cap W^{2,2}$ surface achieving the inﬁmum of the problem when the weight $\Lambda$ is suﬃciently small.

Keywords: area functional, Willmore functional