Multiscale Relaxation of Convex Functionals
Irene Fonseca, Elvira Zappale · Journal of convex analysis · 2003
The \Gamma Γ -limit of a family of functionals u\mapsto \int_{\Omega}f\left(\frac{x}{\varepsilon},\frac{x}{\varepsilon^2},D^su\right)\, dx u ↦ ∫ Ω f ( x ε , x ε 2 , D s u ) d x is obtained for s=1,2 s = 1 , 2 and when the integrand f=f(x,y,v) f = f ( x , y , v ) is a continuous function, periodic in x x and y y , and convex with respect to v v . The 3 3 -scale limits of second order derivatives are characterized.