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Pereira","submitted_at":"2011-04-01T04:30:09Z","abstract_excerpt":"In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^\\epsilon = \\{(x_1,x_2) \\in \\R^2 \\; | \\; x_1 \\in (0,1), \\, - \\, \\epsilon \\, b(x_1) < x_2 < \\epsilon \\, G(x_1, x_1/\\epsilon^\\alpha) \\}$ with $\\alpha>1$ and $\\epsilon > 0$, defined by smooth functions $b(x)$ and $G(x,y)$, where the function $G$ is supposed to be $l(x)$-periodic in the second variable $y$. The condition $\\alpha > 1$ implies that the upper boundary of this thin domain presents a very high oscillatory behavior. 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