Volume 17, Number 4, October-December 2011
|Page(s)||1158 - 1173|
|Published online||28 October 2010|
Scaling laws for non-Euclidean plates and the W2,2 isometric immersions of Riemannian metrics
University of Minnesota, Department of Mathematics,
206 Church St. S.E., Minneapolis, MN 55455, USA. firstname.lastname@example.org
2 University of Pittsburgh, Department of Mathematics, 139 University Place, Pittsburgh, PA 15260, USA. email@example.com
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 Γ-convergence under the proper scaling. As a corollary, we obtain new necessary and sufficient conditions for existence of a W2,2 isometric immersion of a given 2d metric into .
Mathematics Subject Classification: 74K20 / 74B20
Key words: Non-Euclidean plates / nonlinear elasticity / Gamma convergence / calculus of variations / isometric immersions
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.