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Abstract:

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.

Registro:

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

Referencias:

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Citas:

---------- APA ----------
Bonder, J.F., Dozo, E.L. & Rossi, J.D. (2004) . Symmetry properties for the extremals of the Sobolev trace embedding. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 21(6), 795-805.
http://dx.doi.org/10.1016/j.anihpc.2003.09.005
---------- CHICAGO ----------
Bonder, J.F., Dozo, E.L., Rossi, J.D. "Symmetry properties for the extremals of the Sobolev trace embedding" . Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire 21, no. 6 (2004) : 795-805.
http://dx.doi.org/10.1016/j.anihpc.2003.09.005
---------- MLA ----------
Bonder, J.F., Dozo, E.L., Rossi, J.D. "Symmetry properties for the extremals of the Sobolev trace embedding" . Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 21, no. 6, 2004, pp. 795-805.
http://dx.doi.org/10.1016/j.anihpc.2003.09.005
---------- VANCOUVER ----------
Bonder, J.F., Dozo, E.L., Rossi, J.D. Symmetry properties for the extremals of the Sobolev trace embedding. Anna Inst Henri Poincare Annal Anal Non Lineaire. 2004;21(6):795-805.
http://dx.doi.org/10.1016/j.anihpc.2003.09.005