Symmetry properties for the extremals of the Sobolev trace embedding
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...
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I28-R145-paper_02941449_v21_n6_p795_Bonder_oai2024-08-16 Bonder, J.F. Dozo, E.L. Rossi, J.D. 2004 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. application/pdf http://hdl.handle.net/20.500.12110/paper_02941449_v21_n6_p795_Bonder info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Anna Inst Henri Poincare Annal Anal Non Lineaire 2004;21(6):795-805 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 Symmetry properties for the extremals of the Sobolev trace embedding info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_02941449_v21_n6_p795_Bonder_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| 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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_02941449_v21_n6_p795_Bonder_oai |
| work_keys_str_mv |
AT bonderjf symmetrypropertiesfortheextremalsofthesobolevtraceembedding AT dozoel symmetrypropertiesfortheextremalsofthesobolevtraceembedding AT rossijd symmetrypropertiesfortheextremalsofthesobolevtraceembedding |
| _version_ |
1809357001009922048 |