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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todo:paper_02941449_v21_n6_p795_Bonder2023-10-03T15:17:19Z Symmetry properties for the extremals of the Sobolev trace embedding 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. JOUR 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) |
| 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 |
JOUR |
| 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 |
| 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_ |
1807316348084158464 |