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
收藏
页数：26
相关论文
共 50 条
12345