Boundary value problems for Willmore curves in \(\mathbb {R}^2\)
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Publication:5963594
DOI10.1007/s00526-015-0925-zzbMath1362.53010arXiv1501.03976OpenAlexW1527489603MaRDI QIDQ5963594
Publication date: 22 February 2016
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1501.03976
Optimization of shapes other than minimal surfaces (49Q10) Curves in Euclidean and related spaces (53A04) Boundary value problems for functional-differential equations (34K10)
Related Items (9)
Willmore Obstacle Problems under Dirichlet Boundary Conditions ⋮ Some minimization problems for planar networks of elastic curves ⋮ Periodic solutions to a Cahn-Hilliard-Willmore equation in the plane ⋮ Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution ⋮ Elastic curves and phase transitions ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ An obstacle problem for elastic curves: existence results ⋮ Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions ⋮ Stability of stationary points for one-dimensional Willmore energy with spatially heterogeneous term
Cites Work
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- Unstable Willmore surfaces of revolution subject to natural boundary conditions
- Explicit elastic curves
- Willmore surfaces of revolution with two prescribed boundary circles
- The Willmore boundary problem
- Boundary value problems for the one-dimensional Willmore equation
- Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
- Stability and Symmetry in the Navier Problem for the One-Dimensional Willmore Equation
- A Navier boundary value problem for Willmore surfaces of revolution
- Classical solutions to the Dirichlet problem for Willmore surfaces of revolution
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