The Helfrich boundary value problem

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 res...

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Published in:Calculus of variations and partial differential equations 2019-02, Vol.58 (1), p.1-26, Article 34
Main Author: Eichmann, Sascha
Format: Article
Language:English
Subjects:
Analysis
Boundary conditions
Boundary value problems
Calculus of Variations and Optimal Control
Optimization
Control
Dirichlet problem
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Submerging
Systems Theory
Theoretical
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description 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 Große-Brauckmann.
doi_str_mv 10.1007/s00526-018-1468-x
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subjects Analysis
Boundary conditions
Boundary value problems
Calculus of Variations and Optimal Control
Optimization
Control
Dirichlet problem
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Submerging
Systems Theory
Theoretical
title The Helfrich boundary value problem
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