Minimising a relaxed Willmore functional for graphs subject to boundary conditions

DOI10.4171/IFB/378zbMath1368.49046arXiv1503.01275OpenAlexW2963922186MaRDI QIDQ2360099

Matthias Röger, Hans-Christoph Grunau, Klaus Deckelnick

Publication date: 23 June 2017

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.01275

zbMATH Keywords

graphboundary conditionsrelaxationlower semicontinuityWillmore functionalarea estimatediameter estimateexistence of a minimiser

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (11)

Willmore Obstacle Problems under Dirichlet Boundary Conditions ⋮ Lower semicontinuity for the Helfrich problem ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ A resolution of the Poisson problem for elastic plates ⋮ Phase field models for thin elastic structures with topological constraint ⋮ The Helfrich boundary value problem ⋮ Degenerate elastic networks ⋮ Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation ⋮ Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions ⋮ On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves ⋮ Minimisers of Helfrich functional for surfaces of revolution

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