A unique graph of minimal elastic energy

DOI10.1090/S0002-9947-06-04315-7zbMath1110.58009OpenAlexW1542984826MaRDI QIDQ3420389

Anders Linnér, Joseph W. Jerome

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-06-04315-7

zbMATH Keywords

elastic energyphase constraintsEuler-Lagrange equationobstaclependulum equationHamiltonian global minimumone-dimensional Willmore equation

Mathematics Subject Classification ID

Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Applications of global analysis to the sciences (58Z05) Applications of variational problems to control theory (58E25)

Related Items (7)

Elastic splines. II. Unicity of optimal s-curves and curvature continuity ⋮ Some minimization problems for planar networks of elastic curves ⋮ \(L^2\)-flow of elastic curves with clamped boundary conditions ⋮ Boundary value problems for Euler-Bernoulli planar elastica. A solution construction procedure ⋮ Elastic splines III: existence of stable nonlinear splines ⋮ Elastic curves and phase transitions ⋮ A new diffuse-interface approximation of the Willmore flow

Cites Work

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• Curve-straightening in Riemannian manifolds
• Unified representations of nonlinear splines
• Smooth Interpolating Curves of Prescribed Length and Minimum Curvature
• Existence of free nonclosed Euler–Bernoulli elastica

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