Calculus of Variations and Geometric Measure Theory

L. Freddi - R. Paroni

A 3D-1D Young measure theory of an elastic string

created on 16 Jul 2003
modified by freddi on 16 Dec 2004


Published Paper

Inserted: 16 jul 2003
Last Updated: 16 dec 2004

Journal: Asymptotic Analysis
Volume: 39
Number: 1
Pages: 61-89
Year: 2004


A variational limit defined on the space of one-dimensional Young measures is obtained from three-dimensional elasticity via dimension reduction. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account.\ The rate at which it blows up characterizes the domain of the limit energy.\ The obtained limit problem uniquely determines the energy density of the elastic string.

Keywords: Young Measures, $\Gamma$-convergence, dimension reduction, nonlinear elasticity