Calculus of Variations and Geometric Measure Theory
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M. Pozzetta

Confined Willmore energy and the Area functional

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



Inserted: 19 oct 2017
Last Updated: 17 oct 2018

Year: 2018


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


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