Generalised twists, \(\mathrm {SO}(n)\), and the \(p\)-energy over a space of measure preserving maps

DOI10.1016/j.anihpc.2009.03.003zbMath1172.74021OpenAlexW2085737439MaRDI QIDQ732527

Mohammad Sadegh Shahrokhi-Dehkordi, Ali Taheri

Publication date: 9 October 2009

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

Full work available at URL: https://eudml.org/doc/78918

zbMATH Keywords

Euler-Lagrange equationsuniquenessnon-uniquenesseven dimensionsodd dimensions

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Existence theories for free problems in two or more independent variables (49J10)

Related Items (9)

Geodesics on \(\mathrm{SO}(n)\) and a class of spherically symmetric maps as solutions to a nonlinear generalised harmonic map problem ⋮ Topology of twists, extremising twist paths and multiple solutions to the nonlinear system in variation \(\mathscr{L}[u = \nabla \mathscr{P}\)] ⋮ The existence of multiple topologically distinct solutions to \(\sigma_{2, p}\)-energy ⋮ Annular rearrangements, incompressible axi-symmetric whirls and \(L^1\)-local minimisers of the distortion energy ⋮ Twist maps as energy minimisers in homotopy classes: symmetrisation and the coarea formula ⋮ On critical points of the \(\sigma_2\)-energy over a space of measure preserving maps ⋮ Homotopy classes of self-maps of annuli, generalised twists and spin degree ⋮ Generalised twists, stationary loops, and the Dirichlet energy over a space of measure preserving maps ⋮ On the existence and multiplicity of topologically twisting incompressible $H$-harmonic maps and a structural H-condition

Cites Work

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• Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity
• Convexity conditions and existence theorems in nonlinear elasticity
• On the partial regularity of energy-minimizing, area-preserving maps
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• Maximum Principles And A priori Estimates For An Incompressible Material In Nonlinear Elasticity
• On homotopy conditions and the existence of multiple equilibria in finite elasticity

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