A corrector result for an electrostatic model of interdigitated combs

Abstract

In this article, we consider two opposite and intergitated 2D-combs, each one with ε-periodically distributed fingers, each finger having cross-section of order ε and fixed height. Via an asymptotic analysis based on the two-scale convergence method, we study, as ε vanishes, the electrical potential in the vacuum between these two combs when one comb is grounded while the voltage in the other one is assumed of order ε, and we prove a corrector result.

Keywords:

• Electrical potential
• rough boundary
• homogenization

2020 Mathematics Subject Classifications:

• 35J05
• 35B27

Acknowledgments

This research was supported by the project ‘Start’ within the program of the University ‘Luigi Vanvitelli’ reserved to young researchers, Piano strategico 2021-2023.

Disclosure statement

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