Uniqueness for the homogeneous Dirichlet Willmore boundary value problem

DOI10.1007/S10455-012-9320-6zbMath1255.35008OpenAlexW2080671736MaRDI QIDQ1759455

Anna Dall'Acqua

Publication date: 20 November 2012

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-012-9320-6

zbMATH Keywords

Dirichlet boundary conditionsWillmore surfacesconformal invariancePohozaev identity

Mathematics Subject Classification ID

Initial value problems for nonlinear higher-order PDEs (35G25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (9)

Local solutions to a free boundary problem for the Willmore functional ⋮ Noether's theorem and the Willmore functional ⋮ Nonuniqueness for Willmore surfaces of revolution satisfying Dirichlet boundary data ⋮ Stationary surfaces with boundaries ⋮ Sufficient conditions for Willmore immersions in \(\mathbb R^3\) to be minimal surfaces ⋮ Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary ⋮ Elastic curves and phase transitions ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves

Cites Work

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• Existence of surfaces minimizing the Willmore functional
• The Willmore boundary problem
• Uniqueness theorems for Willmore surfaces with fixed and free boundaries
• Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
• Boundary value problems for variational integrals involving surface curvatures
• A Navier boundary value problem for Willmore surfaces of revolution
• Classical solutions to the Dirichlet problem for Willmore surfaces of revolution
• Riemannian geometry and geometric analysis

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