The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Volumn 138, Issue 2, 2008, Pages 223-237

  Arrieta, José M ^a   Rodríguez Bernal, Aníbal ^a   Rossi, J D ^b,c  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^c UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48849110194     PISSN: 03082105     EISSN: 14737124     Source Type: Journal    
DOI: 10.1017/S0308210506000813     Document Type: Article

References (15)

1. J. M. Arrieta, A. Jiménez-Casas and A. Rodríguez-Bernal. Nonhomogeneous flux condition as limit of concentrated reactions. Rev. Mat. Ibero (In the press.)
2. P. Cherrier. Problèmes de Neumann non linéaires sur les variétés Riemanniennes. J. Funct. Analysis 57 (1984), 154-206.
3. M. del Pino and C. Flores. Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains. Commun. PDEs 26 (2001), 2189-2210.
4. J. Fernández Bonder and J. D. Rossi. Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains. Commun. Pure Appl. Analysis 1 (2002), 359-378.
5. J. Fernández Bonder and J. D. Rossi. On the existence of extremals for the Sobolev trace embedding theorem with critical exponent. Bull. Lond. Math. Soc. 37 (2005), 119-125.
6. J. Fernández Bonder, E. Lami Dozo and J. D. Rossi. Symmetry properties for the extremals of the Sobolev trace embedding. Annales Inst. H. Poincaré Analyse Non Linéaire 21 (2004), 795-805.
7. B. Kawohl. Symmetry results for functions yielding best constants in Sobolev-type inequalities. Discrete Contin. Dynam. Syst. A 6 (2000), 683-690. (Erratum 17 (2007), 690.)
8. O. Ladyzhenskaya and N. Uralseva. Linear and quasilinear elliptic equations (Academic, 1968).
9. E. Lami Dozo and O. Torne. Symmetry and symmetry breaking for minimizers in the trace inequality. Commun. Contemp. Math. 7 (2005), 727-746.
10. Y. Li and M. Zhu. Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries. Commun. Pure Appl. Math. 50 (1997), 449-487.
11. S. Martinez and J. D. Rossi. Isolation and simplicity for the first eigenvalue of the p-laplacian with a nonlinear boundary condition. Abstr. Appl. Analysis 7 (2002), 287-293.
12. A. Rodríguez-Bernal and A. Vidal-Lopez. Extremal equilibria for parabolic nonlinear reaction diffusion equations. Proc. Equadiff 11, Bratislava, Slovakia (ed. M. Fila, A. Handlovicova, K. Mikula, M. Medved, P. Quittner and D. Sevcovic), pp. 531-539 (Bratislava: Comenius University Press, 2007).
13. A. Rodríguez-Bernal and A. Vidal-Lopez. Extremal equilibria for nonlinear parabolic equations and applications. Preprint MA-UCM-2006-6, Universidad Complutense de Madrid.
14. M. W. Steklov. Sur les problèmes fondamentaux en physique mathématique. Annales Scient. Éc. Norm. Sup. 19 (1902), 455-490.
15. A. Vidal-Lopez. Soluciones extremales para problemas parabolicos de evolucion no lineales y aplicaciones. PhD thesis, Departamento de Matemática Aplicada, Universidad Complutense de Madrid (2005).