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Arrieta, J.M.; Rodríguez-Bernal, A.; Rossi, J.D. "The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary" (2008) Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 138(2):223-237
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Abstract:

In this paper we prove that the best constant in the Sobolev trace embedding H1(Ω) → Lq(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H1(Ω) → Lq(ωε, dx/ε), where ω ε = {x ∈ Ω: dist (x, ∂Ω) < ε} is a small neighbourhood of the boundary. We also analyse symmetry properties of extremals of the latter embedding when Ω is a ball. © 2008 The Royal Society of Edinburgh.

Registro:

Documento: Artículo
Título:The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary
Autor:Arrieta, J.M.; Rodríguez-Bernal, A.; Rossi, J.D.
Filiación:Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain
Departamento de Matemática, Facultad de Ciencias Exactas Y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
IMDEA-Matemáticas, C-IX, Universidad Autónoma de Madrid, Campus Cantoblanco, Madrid, Spain
Año:2008
Volumen:138
Número:2
Página de inicio:223
Página de fin:237
DOI: http://dx.doi.org/10.1017/S0308210506000813
Título revista:Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Título revista abreviado:Proc. R. Soc. Edinburgh Sect. A Math.
ISSN:03082105
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v138_n2_p223_Arrieta

Referencias:

  • Arrieta, J.M., Jiménez-Casas, A., Rodríguez-Bernal, A., Nonhomogeneous flux condition as limit of concentrated reactions Rev. Mat. Ibero, , In the press
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  • Fernández Bonder, J., Rossi, J.D., Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains (2002) Commun. Pure Appl. Analysis, 1, pp. 359-378
  • Fernández Bonder, J., Rossi, J.D., On the existence of extremals for the Sobolev trace embedding theorem with critical exponent (2005) Bull. Lond. Math. Soc, 37, pp. 119-125
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  • 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.); Ladyzhenskaya, O., Uralseva, N., (1968) Linear and quasilinear elliptic equations, , Academic
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  • 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); A. Rodríguez-Bernal and A. Vidal-Lopez. Extremal equilibria for nonlinear parabolic equations and applications. Preprint MA-UCM-2006-6, Universidad Complutense de Madrid; Steklov, M.W., Sur les problèmes fondamentaux en physique mathématique. (1902) Annales Scient. Éc. Norm. Sup, 19, pp. 455-490
  • Vidal-Lopez, A., (2005) Soluciones extremales para problemas parabolicos de evolucion no lineales y aplicaciones, , PhD thesis, Departamento de Matemática Aplicada, Universidad Complutense de Madrid

Citas:

---------- APA ----------
Arrieta, J.M., Rodríguez-Bernal, A. & Rossi, J.D. (2008) . 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, 138(2), 223-237.
http://dx.doi.org/10.1017/S0308210506000813
---------- CHICAGO ----------
Arrieta, J.M., Rodríguez-Bernal, A., Rossi, J.D. "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 138, no. 2 (2008) : 223-237.
http://dx.doi.org/10.1017/S0308210506000813
---------- MLA ----------
Arrieta, J.M., Rodríguez-Bernal, A., Rossi, J.D. "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, vol. 138, no. 2, 2008, pp. 223-237.
http://dx.doi.org/10.1017/S0308210506000813
---------- VANCOUVER ----------
Arrieta, J.M., Rodríguez-Bernal, A., Rossi, J.D. The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary. Proc. R. Soc. Edinburgh Sect. A Math. 2008;138(2):223-237.
http://dx.doi.org/10.1017/S0308210506000813