Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we study the best constant of the Sobolev trace embedding H 1 (Ω) → L 2 (∂Ω), where Ω is a bounded smooth domain in ℝ N . We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we consider deformations that preserve volume. © Canadian Mathematical Society 2008.

Registro:

Documento: Artículo
Título:First variations of the best Sobolev trace constant with respect to the domain
Autor:Rossi, J.D.
Filiación:Departamento de Matemática, FCEyN UBA, (1428) Buenos Aires, Argentina
Palabras clave:Nonlinear boundary conditions; Sobolev trace embedding
Año:2008
Volumen:51
Número:1
Página de inicio:140
Página de fin:145
DOI: http://dx.doi.org/10.4153/CMB-2008-016-5
Título revista:Canadian Mathematical Bulletin
Título revista abreviado:Can. Math. Bull.
ISSN:00084395
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00084395_v51_n1_p140_Rossi

Referencias:

  • Adimurthi and S. L. Yadava, Positive solution for Neumann problem with critical non linearity on boundary. Comm. Partial Differential Equations, 16(1991), no. 11, 1733-1760; Aubin, T., Équations différentielles non linéaires et le problème de Yamabe concernant la courbure scalaire (1976) J. Math. Pures Appl, 55 (3), pp. 269-296
  • Biezuner, R.J., Best constants in Sobolev trace inequalities (2003) Nonlinear Anal, 54 (3), pp. 575-589
  • Druet, O., Hebey, E., The AB program in geometric analysis: Sharp Sobolev inequalities and related problems (2002) Mem. Amer. Math. Soc, 160 (761)
  • del Pino, M., Flores, C., Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains (2001) Comm. Partial Differential Equations, 26 (11-12), pp. 2189-2210
  • Escobar, J.F., Sharp constant in a Sobolev trace inequality (1988) Indiana Math. J, 37 (3), pp. 687-698
  • Fernández Bonder, J., Lami Dozo, E., Rossi, J.D., Symmetry properties for the extremals of the Sobolev trace embedding (2004) Ann. Inst. H. Poincaré. Anal. Non Linéaire, 21 (6), pp. 795-805
  • Fernández Bonder, J., Rossi, J.D., Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains (2002) Comm. Pure Appl. Anal, 1 (3), 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. London Math. Soc, 37 (1), pp. 119-125
  • García-Melián, J., Sabina de Lis, J., On the perturbation of eigenvalues for the p-Laplacian (2001) C. R. Acad. Sci. Paris Sér I Math, 332 (10), pp. 893-898
  • Henrot, A., Minimization problems for eigenvalues ofthe Laplacian (2003) J. Evol. Equ, 3 (3), pp. 443-461
  • Henrot, A., Pierre, M., Variation et optimization deformes: Une analyse géométrique (2005) Mathématiques et Applications, 48. , Springer, New York
  • Kato, T., (1995) Perturbation theory for linear operators, , Springer-Verlag, Berlin
  • Lami Dozo, E., Tome, O., Symmetry and symmetry breaking for minimizers in the trace inequality (2005) Commun. Contemp. Math, 7 (6), pp. 727-746
  • Li, Y., Zhu, M., Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries (1997) Comm. Pure Appl. Math, 50 (5), pp. 449-487
  • Martinez, S., Rossi, J.D., Isolation and simplicity for the first eigenvalue of the p-laplacian with a nonlinear boundary condition (2002) Abstr. Appl. Anal, 7 (5), pp. 287-293

Citas:

---------- APA ----------
(2008) . First variations of the best Sobolev trace constant with respect to the domain. Canadian Mathematical Bulletin, 51(1), 140-145.
http://dx.doi.org/10.4153/CMB-2008-016-5
---------- CHICAGO ----------
Rossi, J.D. "First variations of the best Sobolev trace constant with respect to the domain" . Canadian Mathematical Bulletin 51, no. 1 (2008) : 140-145.
http://dx.doi.org/10.4153/CMB-2008-016-5
---------- MLA ----------
Rossi, J.D. "First variations of the best Sobolev trace constant with respect to the domain" . Canadian Mathematical Bulletin, vol. 51, no. 1, 2008, pp. 140-145.
http://dx.doi.org/10.4153/CMB-2008-016-5
---------- VANCOUVER ----------
Rossi, J.D. First variations of the best Sobolev trace constant with respect to the domain. Can. Math. Bull. 2008;51(1):140-145.
http://dx.doi.org/10.4153/CMB-2008-016-5