English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Motivated by certain mathematical models for Micro-Electro-Mechanical Systems(MEMS), we give upper and lower $L^\infty$ estimates for the minimal solutionsof nonlinear eigenvalue problems of the form $-\Delta u = \lambda f(x) F(u)$ ona smooth bounded domain $ \Omega$ in $\IR^N$. We are mainly interested in the{\it pull-in distance}, that is the $L^\infty-$norm of the extremal solution$u^*$ and how it depends on the geometry of the domain, the dimension of thespace, and the so-called {\it permittivity profile} $f$. In particular, ourresults provide mathematical proofs for various observed phenomena, as well asrigorous derivations for several estimates obtained numerically by Pelesko\cite{P}, Guo-Pan-Ward \cite{GPW} and others in the case of the MEMSnon-linearity $F(u)=\frac{1}{(1-u)^2}$ and for power-law permittivity profiles$f(x)=|x|^\alpha$.

Estimates on Pull-in Distances in MEMS Models and other Nonlinear Eigenvalue Problems