Minimisers of Helfrich functional for surfaces of revolution

DOI10.3934/CPAA.2022074zbMath1498.49078OpenAlexW4226531437MaRDI QIDQ2087555

Hongbo Zeng, Huai-Yu Jian

Publication date: 21 October 2022

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2022074

zbMATH Keywords

variational problemDirichlet boundary value problemfourth order equationHelfrich functional

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Existence theories for free problems in two or more independent variables (49J10) PDEs in connection with quantum mechanics (35Q40) Optimization of shapes other than minimal surfaces (49Q10)

Cites Work

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• Existence and uniqueness for variational problem from progressive Lens design
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• Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions
• Minimising a relaxed Willmore functional for graphs subject to boundary conditions
• The Willmore boundary problem
• Min-max theory and the Willmore conjecture
• Some remarks on Willmore surfaces embedded in \(\mathbb R^3\)
• Closed surfaces with bounds on their Willmore energy
• Global minimizers for axisymmetric multiphase membranes
• Irrationality of certain infinite series II

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