Extremal functions for the anisotropic Sobolev inequalities. Fonctions minimales pour des inégalités de Sobolev anisotropiques
نویسنده
چکیده
The existence of multiple nonnegative solutions to the anisotropic critical problem
منابع مشابه
Fonctions minimales pour des inégalités de Sobolev anisotropiques
The existence of multiple nonnegative solutions to the anisotropic critical problem − N ∑ i=1 ∂ ∂xi ∣∣∣∣ ∂u ∂xi ∣∣∣∣pi−2 ∂u ∂xi ) = |u|p−2u in R is proved in suitable anisotropic Sobolev spaces. The solutions correspond to extremal functions of a certain best Sobolev constant. The main tool in our study is an adaptation of the well-known concentration-compactness lemma of P.-L. Lions to anisotr...
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تاریخ انتشار 2008