Calculus of Variations and Geometric Measure Theory

I. Fonseca - E. Zappale

Multiscale Relaxation of Convex Functionals

created on 11 Dec 2002
modified on 12 Jan 2004


Published Paper

Inserted: 11 dec 2002
Last Updated: 12 jan 2004

Journal: Journal of Convex Analysis
Volume: 10
Number: 2
Pages: 325-350
Year: 2002


The $\Gamma$-limit of a family of functionals $$ u\mapsto \int{\Omega}f\left({\frac{x}{\varepsilon}},{\frac{x}{{\varepsilon}2}},Ds u\right)\, dx $$ is obtained for $s=1,2$ and when the integrand $f=f(x,y,v)$ is a continuous function, periodic in $x$ and $y$, and convex with respect to $v$. The $3$-scale limits of second order derivatives are cha