# American Institute of Mathematical Sciences

November  2012, 32(11): 3819-3839. doi: 10.3934/dcds.2012.32.3819

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

 1 Departamento de Matemática Aplicada y Computación, Escuela Técnica Superior de Ingeniería - ICAI, Universidad Ponti cia Comillas, Alberto Aguilera, 25, 28015-Madrid, Spain

Received  July 2011 Revised  October 2011 Published  June 2012

In this paper is proved that the Strong Maximum Principle is satisfied for a wide class of linear elliptic boundary value problems of mixed type in an annulus of $\mathbb{R}^N$, $N\geq 1$, provided it is thin enough. The coercive character of these boundary value problems is obtained thanks to the characterization of the Strong Maximum Principle found in [3], proving that the principal eigenvalue associated to each boundary value problem may be as large as we wish, independently of the weight on the boundary, by taking the annulus thin enough.
Citation: Santiago Cano-Casanova. Coercivity of elliptic mixed boundary value problems in annulus of $\mathbb{R}^N$. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3819-3839. doi: 10.3934/dcds.2012.32.3819
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