Coercivity of elliptic mixed boundary value problems in annulus of $\mathbb{R}^N$

Abstract

In this paper is proved that the Strong Maximum Principle issatisfied for a wide class of linear elliptic boundary valueproblems of mixed type in an annulus of $\mathbb{R}^N$, $N\geq 1$,provided it is thin enough. The coercive character of theseboundary value problems is obtained thanks to the characterizationof the Strong Maximum Principle found in [3], proving thatthe principal eigenvalue associated to each boundary value problemmay be as large as we wish, independently of the weight on theboundary, by taking the annulus thin enough.