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April, 2008 Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary
José M. Arrieta , Ángela Jiménez-Casas , Aníbal Rodríguez-Bernal
Rev. Mat. Iberoamericana 24(1): 183-211 (April, 2008).

Abstract

We analyze the limit of the solutions of an elliptic problem when some reaction and potential terms are concentrated in a neighborhood of a portion $\Gamma$ of the boundary and this neighborhood shrinks to $\Gamma$ as a parameter goes to zero. We prove that this family of solutions converges in certain Sobolev spaces and also in the sup norm, to the solution of an elliptic problem where the reaction term and the concentrating potential are transformed into a flux condition and a potential on $\Gamma$.

Citation

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José M. Arrieta . Ángela Jiménez-Casas . Aníbal Rodríguez-Bernal . "Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary." Rev. Mat. Iberoamericana 24 (1) 183 - 211, April, 2008.

Information

Published: April, 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1162.35021
MathSciNet: MR2435970

Subjects:
Primary: 35B20 , 35J25

Keywords: boundary potential , boundary reaction , concentrating terms , elliptic equations

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 1 • April, 2008
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