Planar \textit{p}-elastic curves and related generalized complete elliptic integrals

DOI10.2996/KMJ/1404393898zbMath1294.49003OpenAlexW2041222844MaRDI QIDQ740768

Kohtaro Watanabe

Publication date: 9 September 2014

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.kmj/1404393898

zbMATH Keywords

elliptic functionsdifferential geometrysoliton theorymaterial mechanicsLebesgue \({L}^{2}\) caseplanar elastica problem

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Geometric methods (93B27) Classical linear elasticity (74B05) Variational problems in a geometric measure-theoretic setting (49Q20) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items (9)

Symplectically convex and symplectically star-shaped curves: a variational problem ⋮ Polar tangential angles and free elasticae ⋮ A remark on the first \(p\)-buckling eigenvalue with an adhesive constraint ⋮ A regularized gradient flow for the \(p\)-elastic energy ⋮ A relation between cylindrical critical points of Willmore-type energies, weighted areas and vertical potential energies ⋮ A gradient flow for the \(p\)-elastic energy defined on closed planar curves ⋮ The \(p\)-elastic flow for planar closed curves with constant parametrization ⋮ Monotonicity properties and bounds for the complete \(p\)-elliptic integrals ⋮ The critical points of the elastic energy among curves pinned at endpoints

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