Calculus of Variations and Geometric Measure Theory

G. Cardone - A. Corbo Esposito - V. V. Zhikov

A compactness result for a class of nonstandard lagrangians in the case of elasticity

created on 10 Jan 2002


Submitted Paper

Inserted: 10 jan 2002

Journal: Applicable Analysis
Year: 2001



A general compactness result, with respect to $\Gamma -$convergence,

is proved for a family of functionals of the C.o.V. in the case

of elasticity, i.e. for functionals of the type $f(x,e(u))$, where

the integrand $f$, convex in the second variable,

satisfies nonstandard growth conditions, $u$ is a vector-valued functions

and $e(u)$ is the strain tensor. An (abstract) representation of the

$\Gamma -$limit is also given.