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 $\Gamma$.
@article{1216247099,
author = {Arrieta , Jos\'e M. and Jim\'enez-Casas , \'Angela and Rodr\'\i guez-Bernal , An\'\i bal},
title = {Flux terms and Robin boundary conditions as limit of
reactions and potentials concentrating at the boundary},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 183-211},
language = {en},
url = {http://dml.mathdoc.fr/item/1216247099}
}
Arrieta , José M.; Jiménez-Casas , Ángela; Rodríguez-Bernal , Aníbal. Flux terms and Robin boundary conditions as limit of
reactions and potentials concentrating at the boundary. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 183-211. http://gdmltest.u-ga.fr/item/1216247099/