Convergence of energy minimizers of a MEMS model in the reinforced limit

TL;DR

This paper proves that energy minimizers in a MEMS model with an insulating layer converge to the minimizer of a limiting model as the layer's thickness approaches zero, using $ ext{Gamma}$-convergence techniques.

Contribution

It establishes the convergence of energy minimizers in a MEMS model with an insulating layer to a limiting model as the layer becomes vanishingly thin, via $ ext{Gamma}$-limit analysis.

Findings

Energy minimizers converge in the reinforced limit

Identification of the $ ext{Gamma}$-limit of the energy

Validation of the limiting model as the layer thickness tends to zero

Abstract

Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends to zero. The proof relies on the identification of the $\Gamma$-limit of the energy in this limit.