The Helfrich boundary value problem

被引：13

作者：

Eichmann, Sascha ^{[1
]}

机构：

[1] Eberhard Karls Univ Tubingen, Math Nat Wissensch Fak, Morgenstelle 10, D-72076 Tubingen, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 58卷 / 01期

关键词：

WILLMORE SURFACES; FUNCTIONALS; MINIMIZERS; EXISTENCE; GRAPHS;

D O I：

10.1007/s00526-018-1468-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a branched Helfrich immersion satisfying Dirichlet boundary conditions. The number of branch points is finite. We proceed by a variational argument and hence examine the Helfrich energy for oriented varifolds. The main contribution of this paper is a lower semicontinuity result with respect to oriented varifold convergence for the Helfrich energy and a minimising sequence. For arbitrary sequences this is false by a counterexample of Gro ss e-Brauckmann.

引用

页数：26

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