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.

Keywords: nonlinear elasticity, singular minimizer, stability

@article{COCV_2008__14_1_192_0, author = {Yan, Xiaodong and Bevan, Jonathan}, title = {Minimizers with topological singularities in two dimensional elasticity}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {192--209}, publisher = {EDP-Sciences}, volume = {14}, number = {1}, year = {2008}, doi = {10.1051/cocv:2007043}, zbl = {1140.49014}, mrnumber = {2375756}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007043/} }

TY - JOUR AU - Yan, Xiaodong AU - Bevan, Jonathan TI - Minimizers with topological singularities in two dimensional elasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 192 EP - 209 VL - 14 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007043/ UR - https://zbmath.org/?q=an%3A1140.49014 UR - https://www.ams.org/mathscinet-getitem?mr=2375756 UR - https://doi.org/10.1051/cocv:2007043 DO - 10.1051/cocv:2007043 LA - en ID - COCV_2008__14_1_192_0 ER -

%0 Journal Article %A Yan, Xiaodong %A Bevan, Jonathan %T Minimizers with topological singularities in two dimensional elasticity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 192-209 %V 14 %N 1 %I EDP-Sciences %U https://doi.org/10.1051/cocv:2007043 %R 10.1051/cocv:2007043 %G en %F COCV_2008__14_1_192_0

Yan, Xiaodong; Bevan, Jonathan. Minimizers with topological singularities in two dimensional elasticity. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 1, pp. 192-209. doi : 10.1051/cocv:2007043. http://www.numdam.org/articles/10.1051/cocv:2007043/

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