The $Gamma$- limit of a family of functionals $int_Omegaf(x/arepsilonx/{arespilon^2} ;D^su)dx$ 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 characterized.
Multiscale Relaxation of Convex Functional / Fonseca, I.; Zappale, Elvira. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 10/2:(2003), pp. 325-350.
Multiscale Relaxation of Convex Functional
ZAPPALE, ELVIRA
2003
Abstract
The $Gamma$- limit of a family of functionals $int_Omegaf(x/arepsilonx/{arespilon^2} ;D^su)dx$ 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 characterized.File allegati a questo prodotto
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