Minimizers with topological singularities in two dimensional elasticity

Yan, Xiaodong; Bevan, Jonathan

ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 1, pp. 192-209.

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 $det\nabla u$ vanishes at one point.

Classification : 49K15, 49K20, 49J30, 74B20
Mots clés : nonlinear elasticity, singular minimizer, stability

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