Symmetry properties for the extremals of the Sobolev trace embedding

Mostrar todas las versiones(3)

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Bonder, J.F., Dozo, E.L., Rossi, J.D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2004
Materias:
Nonlinear boundary conditions
Sobolev trace embedding
Bessel functions
Boundary value problems
Eigenvalues and eigenfunctions
Mathematical models
Problem solving
Theorem proving
Boundary conditions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02941449_v21_n6_p795_Bonder
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_02941449_v21_n6_p795_Bonder
record_format dspace
spelling paperaa:paper_02941449_v21_n6_p795_Bonder2023-06-12T16:47:18Z Symmetry properties for the extremals of the Sobolev trace embedding Anna Inst Henri Poincare Annal Anal Non Lineaire 2004;21(6):795-805 Bonder, J.F. Dozo, E.L. Rossi, J.D. 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 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2004 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02941449_v21_n6_p795_Bonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic 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
spellingShingle 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
Bonder, J.F.
Dozo, E.L.
Rossi, J.D.
Symmetry properties for the extremals of the Sobolev trace embedding
topic_facet 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
description 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.
format Artículo
Artículo
publishedVersion
author Bonder, J.F.
Dozo, E.L.
Rossi, J.D.
author_facet Bonder, J.F.
Dozo, E.L.
Rossi, J.D.
author_sort Bonder, J.F.
title Symmetry properties for the extremals of the Sobolev trace embedding
title_short Symmetry properties for the extremals of the Sobolev trace embedding
title_full Symmetry properties for the extremals of the Sobolev trace embedding
title_fullStr Symmetry properties for the extremals of the Sobolev trace embedding
title_full_unstemmed Symmetry properties for the extremals of the Sobolev trace embedding
title_sort symmetry properties for the extremals of the sobolev trace embedding
publishDate 2004
url http://hdl.handle.net/20.500.12110/paper_02941449_v21_n6_p795_Bonder
work_keys_str_mv AT bonderjf symmetrypropertiesfortheextremalsofthesobolevtraceembedding
AT dozoel symmetrypropertiesfortheextremalsofthesobolevtraceembedding
AT rossijd symmetrypropertiesfortheextremalsofthesobolevtraceembedding
_version_ 1769810286703804416

Ejemplares similares