Publication 16-CNA-011
Periodic Homogenization Of Integral Energies Under Space-Dependent Differential Constraints
Elisa Davoli
Department of Mathematics
University of Vienna
Oskar-Morgenstern-Platz 1
1090 Vienna, Austria
elisa.davoli@univie.ac.at
Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu
Abstract: A homogenization result for a family of oscillating integral
energies
$$ u_{\varepsilon} \rightarrow \int_{\Omega} f(x,
\frac{x}{\varepsilon}, u_{\varepsilon}(x))dx, \ \ \ \varepsilon
\rightarrow 0^+$$
is presented, where the fields $u_{\varepsilon}$ are
subjected to
first order linear differential constraints depending on the space
variable $x$. The work is
based on the theory of ${\cal A}$-quasiconvexity with variable
coefficients and
on two-scale convergence techniques, and generalizes the previously
obtained
results in the case in which the differential constraints are imposed by
means of a linear first order differential operator with constant
coefficients. The identification of the relaxed energy in the framework of
${\cal A}$-quasiconvexity with variable coefficients is also recovered
as a
corollary of the homogenization result.
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