In this article we study symmetry properties of the extremals for the Sobolev trace embedding H1(B(0,μ))→Lq(∂B(0, μ)) with 1≤q≤2(N-1)/(N-2) for different values of μ. These extremals u are solutions of the problem Δu=uinB(0,μ),∂u∂η= λ|u|q-2uon∂B(0,μ). We find that, for 1≤q<2(N-1)/(N-2), there exists a unique normalized extremal u, which is positive and has to be radial, for μ small enough. For the critical case, q=2(N-1)/(N-2), as a consequence of the symmetry properties for small balls, we conclude the existence of radial extremals. Finally, for 1<q≤2, we show that a radial extremal exists for every ball. © 2004 Elsevier SAS. All rights reserved.
Documento: | Artículo |
Título: | Symmetry properties for the extremals of the Sobolev trace embedding |
Autor: | Bonder, J.F.; Dozo, E.L.; Rossi, J.D. |
Filiación: | Departamento de Matemática, FCEyN UBA, (1428) Buenos Aires, Argentina CONICET, Univ. de Buenos Aires, Univ. Libre de Bruxelles, Argentina |
Palabras clave: | Nonlinear boundary conditions; Sobolev trace embedding; Bessel functions; Boundary value problems; Eigenvalues and eigenfunctions; Mathematical models; Problem solving; Theorem proving; Nonlinear boundary conditions; Sobolev trace embedding; Boundary conditions |
Año: | 2004 |
Volumen: | 21 |
Número: | 6 |
Página de inicio: | 795 |
Página de fin: | 805 |
DOI: | http://dx.doi.org/10.1016/j.anihpc.2003.09.005 |
Título revista: | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Título revista abreviado: | Anna Inst Henri Poincare Annal Anal Non Lineaire |
ISSN: | 02941449 |
PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_02941449_v21_n6_p795_Bonder.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02941449_v21_n6_p795_Bonder |