Existence and uniqueness for variational problem from progressive Lens design

DOI10.1007/S11464-020-0845-XzbMath1444.35048OpenAlexW3040096598MaRDI QIDQ777094

Hongbo Zeng, Huai-Yu Jian

Publication date: 3 July 2020

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-020-0845-x

zbMATH Keywords

variational problemDirichlet boundary value problemexistence and uniquenessfourth-order elliptic partial differential equationWillmore surfaces of revolution

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (1)

Minimisers of Helfrich functional for surfaces of revolution

Cites Work

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• The Willmore conjecture
• Symmetry for Willmore surfaces of revolution
• Radially symmetric solutions to the graphic Willmore surface equation
• Symmetric Willmore surfaces of revolution satisfying natural boundary conditions
• A variational approach to progressive lens design.
• Existence of surfaces minimizing the Willmore functional
• The Willmore boundary problem
• Some remarks on Willmore surfaces embedded in \(\mathbb R^3\)
• Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
• Analysis of a Variational Approach to Progressive Lens Design
• A NUMERICAL METHOD FOR PROGRESSIVE LENS DESIGN

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