Artículo
Bonder, J.F.; Rossi, J.D.; Schönlieb, C.-B. "The best constant and extremals of the sobolev embeddings in domains with holes: The L ∞ case" (2008) Illinois Journal of Mathematics. 52(4):1111-1121
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Abstract:
LetΩ⊂ R N be a bounded domain. We study the best constant of the Sobolev trace embedding W 1,∞ (Ω) {right arrow, hooked} L ∞ (∂Ω) for functions that vanish in a subset A ⊂ Ω, which we call the hole. That is we deal with the minimization problem S T A = inf ||u|| W 1,∞ (Ω)/||u||L ∞ (∂Ω) for functions that verify u|A = 0. We find that there exists an optimal hole that minimizes the best constant S T A among subsets of Ω of prescribed volume and we give a geometrical characterization of this optimal hole. In fact, minimizers associated to these holes are cones centered at some points x* 0 on ∂Ω with respect to the arc-length metric in Ω and the best holes are of the form A* =Ω\\B d (x* 0 , r*) where the ball is taken again with respect of the arc-length metric. A similar analysis can be performed for the best constant of the embedding W 1,∞ (Ω) {right arrow, hooked} L ∞ (Ω) with holes. In this case, we also find that minimizers associated to optimal holes are cones centered at some points x* 0 on ∂Ω and the best holes are of the form A*=Ω\\ B d (x* 0 ,r*). © 2009 University of Illinois.
Registro:
| Documento: | Artículo |
| Título: | The best constant and extremals of the sobolev embeddings in domains with holes: The L ∞ case |
| Autor: | Bonder, J.F.; Rossi, J.D.; Schönlieb, C.-B. |
| Filiación: | Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina IMDEA Matematicas, C-IX, Campus UAM, Madrid, Spain Department of Applied Mathematics and Theoretical Physics (DAMTP), Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom |
| Año: | 2008 |
| Volumen: | 52 |
| Número: | 4 |
| Página de inicio: | 1111 |
| Página de fin: | 1121 |
| Título revista: | Illinois Journal of Mathematics |
| Título revista abreviado: | Ill. J. Math. |
| ISSN: | 00192082 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v52_n4_p1111_Bonder |
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Citas:
---------- APA ----------
Bonder, J.F., Rossi, J.D. & Schönlieb, C.-B. (2008) . The best constant and extremals of the sobolev embeddings in domains with holes: The L ∞ case. Illinois Journal of Mathematics, 52(4), 1111-1121.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v52_n4_p1111_Bonder [ ]
---------- CHICAGO ----------
Bonder, J.F., Rossi, J.D., Schönlieb, C.-B. "The best constant and extremals of the sobolev embeddings in domains with holes: The L ∞ case" . Illinois Journal of Mathematics 52, no. 4 (2008) : 1111-1121.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v52_n4_p1111_Bonder [ ]
---------- MLA ----------
Bonder, J.F., Rossi, J.D., Schönlieb, C.-B. "The best constant and extremals of the sobolev embeddings in domains with holes: The L ∞ case" . Illinois Journal of Mathematics, vol. 52, no. 4, 2008, pp. 1111-1121.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v52_n4_p1111_Bonder [ ]
---------- VANCOUVER ----------
Bonder, J.F., Rossi, J.D., Schönlieb, C.-B. The best constant and extremals of the sobolev embeddings in domains with holes: The L ∞ case. Ill. J. Math. 2008;52(4):1111-1121.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v52_n4_p1111_Bonder [ ]
