Calculus of Variations and Geometric Measure Theory

L. Freddi - R. Paroni

The energy density of martensitic thin films via dimension reduction

created on 06 May 2003
modified by freddi on 16 Dec 2004


Published Paper

Inserted: 6 may 2003
Last Updated: 16 dec 2004

Journal: Interfaces and Free Boundaries
Volume: 6
Pages: 439-459
Year: 2004


A variational limit defined on the space of bi-dimensional gradient Young measures is obtained from three-dimensional elasticity via dimension reduction. The obtained limit problem uniquely determines the energy density of the thin film. Our result might be used to compute the microstructure in membranes made of phase transforming material.

Keywords: Young Measures, $\Gamma$-convergence, dimension reduction, martensitic thin film, gradient Young measure