Homogenization of a quasilinear elliptic problem in domains with small holes

Abstract

This work aims to provide the asymptotic behavior of some class of quasilinear problems posed in a domain with small holes in ${\mathbb{R}}^N$ for N>2, as $ϵ\to 0$. A nonlinear Robin boundary condition is prescribed on some of the holes, while a Dirichlet boundary one is imposed on the other holes as well as on the outer boundary. We apply the Periodic Unfolding Method for the homogenization of this problem.

Keywords:

• Homogenization
• nonlinear Robin condition
• periodic unfolding method
• quasilinear problem
• small holes

Mathematics Subject Classification (2020):

• 35B27
• 35J62
• 35M13

Acknowledgments

The first author would like to thank the Department of Science and Technology (DOST) through the Accelerated Science and Technology Human Resource Development Program-National Science Consortium (ASTHRDP-NSC) for funding this work. The authors are also extending their gratitude to the reviewers who gave their inputs in making this paper better.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author would like to thank the Department of Science and Technology (DOST) through the Accelerated Science and Technology Human Resource Development Program-National Science Consortium (ASTHRDP-NSC) for funding this work.