Displaying similar documents to “Remarks on the theory of elasticity”

Topological degree, Jacobian determinants and relaxation

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2005)

Bollettino dell'Unione Matematica Italiana

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A characterization of the total variation T ⁢ V ⁢ u , Ω of the Jacobian determinant det ⁡ D ⁢ u is obtained for some classes of functions u : Ω → R n outside the traditional regularity space W 1 , n ⁢ Ω ; R n . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity x 0 ∈ Ω . Relations between T ⁢ V ⁢ u , Ω and the distributional determinant Det ⁢ D ⁢ u are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps u ∈ W 1 , p ⁢ Ω ; R n ∩ W 1 , ∞ ⁢ Ω x 0 ; R n . ...

Minimizers with topological singularities in two dimensional elasticity

Xiaodong Yan, Jonathan Bevan (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of S 1 ; the minimizer u is C 1 and is such that det ∇ u vanishes at one point.