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arXiv · 1803.11310

The p-Laplacian operator in oscillating thin domains

Jean Carlos Nakasato·Marcone Corrêa Pereira
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Abstract

In this paper we study the asymptotic behavior of the solutions of a class of nonlinear elliptic problems posed in a 2-dimensional domain that degenerates into a line segment (a thin domain) when a positive parameter $\varepsilon$ goes to zero. We also allow high oscillating behavior on the upper boundary of the thin domain as $\varepsilon \to 0$. Combining methods from classic homogenization theory for reticulated structures and monotone operators we obtain the homogenized equation proving convergence of the solutions and establishing a corrector function which guarantees strong convergence in $W^{1,p}$ for $1<p<+\infty$.

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Jean Carlos Nakasato, Marcone Corrêa Pereira. 2018-03-30. The p-Laplacian operator in oscillating thin domains. https://arxiv.org/abs/1803.11310

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