JournalsrmiVol. 24, No. 1pp. 183–211

Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary

  • José M. Arrieta

    Universidad Complutense de Madrid, Spain
  • Angela Jiménez-Casas

    Universidad Pontificia Comillas de Madrid, Spain
  • Aníbal Rodríguez-Bernal

    Universidad Complutense de Madrid, Spain
Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary cover
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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 Γ\Gamma of the boundary and this neighborhood shrinks to Γ\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 Γ\Gamma.

Cite this article

José M. Arrieta, Angela Jiménez-Casas, Aníbal Rodríguez-Bernal, Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 183–211

DOI 10.4171/RMI/533