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Publication 05-CNA-17

The Limit Behavior of a Family of Variational Multiscale Problems

Margarida Baía

and

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Abstract: $ \Gamma$-convergence techniques combined with techniques of $ 2$-scale convergence are used to give a characterization of the behavior as $ \epsilon$ goes to zero of a family of integral functionals defined on $ \Lambda^{p}(\Omega;\mathbb{R}^{d})$ by

\begin{displaymath} {\cal I}_{\epsilon}(u):=\left\{ \begin{array}{l} \displayst... ...\ \\ \infty \hspace{3cm}\mbox{otherwise}, \end{array}\right. \end{displaymath}

under periodicity (and nonconvexity) hypothesis, standard $ p$-coercivity and $ p$-growth conditions with $ p>1$. Uniform continuity with respect to the $ x$ variable, as it is customary in the existing literature, is not required.

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