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Scaling laws for non-euclidean plates and the W 2 , 2 isometric immersions of riemannian metrics

Marta Lewicka;  Mohammad Reza Pakzad — 2011

ESAIM: Control, Optimisation and Calculus of Variations

Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its -convergence under the proper scaling....

Scaling laws for non-Euclidean plates and the isometric immersions of Riemannian metrics

Marta Lewicka;  Mohammad Reza Pakzad — 2011

ESAIM: Control, Optimisation and Calculus of Variations

Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its -convergence under the proper scaling....

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