Extremal functions for the anisotropic Sobolev inequalities

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dc.creatorHamidi, Abdallah El
dc.creatorRakotoson, J. M.
dc.date2008-12-04
dc.date.accessioned2026-07-07T12:43:20Z
dc.date.available2026-07-07T12:43:20Z
dc.descriptionThe existence of multiple nonnegative solutions to the anisotropic critical problem - \sum_{i=1}^{N} \frac{\partial}{\partial x_i} (| \frac{\partial u}{\partial x_i} |^{p_i-2} \frac{\partial u}{\partial x_i}) = |u|^{p^*-2} u {in} \mathbb{R}^N 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 anisotropic operators. Futhermore, we show that the set of nontrival solutions $\calS$ is included in $L^\infty(\R^N)$ and is located outside of a ball of radius $τ>0$ in $L^{p^*}(\R^N)$.
dc.identifierhttps://arxiv.org/abs/0812.0928
dc.identifierhttp://arxiv.org/abs/0812.0928
dc.identifierAnnales de l'Institut Henri Poincaré Analyse non linéaire 24, 5 (2006) 741-756
dc.identifierdoi:10.1016/j.anihpc.2006.06.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220388
dc.subjectAnalysis of PDEs
dc.titleExtremal functions for the anisotropic Sobolev inequalities
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