Characterization and representation of the lower semicontinuous envelope of the elastica functional

DOI10.1016/j.anihpc.2004.01.001zbMath1110.49014OpenAlexW2037084577MaRDI QIDQ1765686

Giovanni Bellettini, Luca Mugnai

Publication date: 23 February 2005

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2004__21_6_839_0

zbMATH Keywords

ElasticaRelaxationSemicontinuityCurvature depending functionals

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Energy minimization in equilibrium problems in solid mechanics (74G65) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (19)

Partial localization, lipid bilayers, and the elastica functional ⋮ Existence, regularity and structure of confined elasticae ⋮ On the approximation of the elastica functional in radial symmetry ⋮ Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case ⋮ On a variational theory of image amodal completion ⋮ The \(L^1\) gradient flow of a generalized scale invariant Willmore energy for radially non-increasing functions ⋮ Overhanging of membranes and filaments adhering to periodic graph substrates ⋮ Total roto-translational variation ⋮ Some minimization problems for planar networks of elastic curves ⋮ A variational model in image processing with focal points ⋮ Convex Lifting-Type Methods for Curvature Regularization ⋮ Phase-field approximations of the Willmore functional and flow ⋮ Confined elasticae and the buckling of cylindrical shells ⋮ Characterization and representation of the lower semicontinuous envelope of the elastica functional ⋮ Locality of the mean curvature of rectifiable varifolds ⋮ Degenerate elastic networks ⋮ TheH^–1-norm of tubular neighbourhoods of curves ⋮ A new diffuse-interface approximation of the Willmore flow ⋮ A varifold perspective on the $p$-elastic energy of planar sets

Cites Work

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• Characterization and representation of the lower semicontinuous envelope of the elastica functional
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