In this paper we study the Sobolev trace embedding W1,p(Ω) → Lp V (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λk / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the study of the second eigenvalue proving that it coincides with the second variational eigenvalue.
@article{urn:eudml:doc:41452,
title = {A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.},
journal = {Publicacions Matem\`atiques},
volume = {46},
year = {2002},
pages = {221-235},
mrnumber = {MR1904864},
zbl = {1014.35070},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41452}
}
Fernández Bonder, Julián; Rossi, Julio D. A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.. Publicacions Matemàtiques, Tome 46 (2002) pp. 221-235. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41452/