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 $\Omega$ nonperiodically. 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.
Acknowledgment
The author thanks to the referees for their suggestions in the improvement of the paper.
Citation
Hiroto Ishida. "Homogenization for Poisson equations in domains with concentrated holes." SUT J. Math. 59 (2) 61 - 71, December 2023. https://doi.org/10.55937/sut/1698476840
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