Euler-lagrange equation and regularity for flat minimizers of the Willmore functional

DOI10.1002/cpa.20342zbMath1209.49061OpenAlexW2167342596MaRDI QIDQ3081314

Peter Hornung

Publication date: 7 March 2011

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

Full work available at URL: https://doi.org/10.1002/cpa.20342

zbMATH Keywords

Riemannian manifoldisometric immersionsWillmore functionalEuler-Lagrange equationregularity propertiesgeometric characterization

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (16)

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Cites Work

• Constrained Willmore surfaces
• Analysis aspects of Willmore surfaces
• Minimizers of Kirchhoff's plate functional: Euler-Lagrange equations and regularity
• Global curvature and self-contact of nonlinearly elastic curves and rods
• Euler-Lagrange equations for nonlinearly elastic rods with self-contact
• On the Sobolev space of isometric immersions
• Removability of point singularities of Willmore surfaces
• Willmore surfaces
• Existence of surfaces minimizing the Willmore functional
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Regularity properties of isometric immersions
• Locking constraints for elastic rods and a curvature bound for spatial curves
• Parameter dependence for a class of ordinary differential equations with measurable right-hand side
• On Spherical Image Maps Whose Jacobians Do Not Change Sign
• Some Rigidity Results Related to Monge–Ampèere Functions
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Nonlinear problems of elasticity
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