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

Santiago Cano-Casanova

doi:10.3934/dcds.2012.32.3819

Article Contents

2012, Volume 32, Issue 11: 3819-3839. Doi: 10.3934/dcds.2012.32.3819

This issue Previous Article Boundary estimates for solutions of weighted semilinear elliptic equations Next Article Dynamics of a reaction-diffusion-advection model for two competing species

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

Santiago Cano-Casanova^1,

1.
Departamento de Matemática Aplicada y Computación, Escuela Técnica Superior de Ingeniería - ICAI, Universidad Ponticia Comillas, Alberto Aguilera, 25, 28015-Madrid

Received: July 2011

Revised: October 2011

Published: November 2012

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Abstract

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.

Keywords:

Maximum principle,
principal eigenvalues,
coercivity of elliptic problems and mixed boundary conditions.

Mathematics Subject Classification: Primary: 34B18, 35P15; Secondary: 34B15, 34B05.

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References

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