Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions

DOI10.1515/acv-2016-0038zbMath1426.49044OpenAlexW2746646733MaRDI QIDQ2328142

Hans-Christoph Grunau, Sascha Eichmann

Publication date: 9 October 2019

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv-2016-0038

zbMATH Keywords

Dirichlet boundary conditionselastic curvesWillmore surfaces of revolutionprojectability

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Nonlinear ordinary differential operators (34L30) Quasilinear elliptic equations (35J62)

Related Items (10)

Stationary surfaces with boundaries ⋮ Willmore Obstacle Problems under Dirichlet Boundary Conditions ⋮ Lower semicontinuity for the Helfrich problem ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ A Li-Yau inequality for the 1-dimensional Willmore energy ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ On the convergence of the elastic flow in the hyperbolic plane ⋮ The Helfrich boundary value problem ⋮ 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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