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arXiv · 2208.04557

Poisson equation in domains with concentrated holes

Hiroto Ishida
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Abstract

We consider solutions $u^\varepsilon$ of Poisson problems with the Dirichlet condition on domains $\Omega_\varepsilon$ with holes concentrated at subsets of a domain $\Omega$ non-periodically. We show $u^\varepsilon$ converges to a solution of a Poisson problem with a simple function potential. This is a generalized result of a sample model given by Cioranescu and Murat (1997). They showed a result for case that holes are distributed at $\Omega$ periodically.

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Hiroto Ishida. 2022-08-09. Poisson equation in domains with concentrated holes. https://doi.org/10.55937/sut/1698476840

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