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Abstract:

In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary. Copyright © Australian Mathematical Society 2007.

Registro:

Documento: Artículo
Título:The best Sobolev trace constant in domains with holes for critical or subcritical exponents
Autor:Fernandezbonder, J.; Orive, R.; Rossi, J.D.
Filiación:Departamento de Matematica, FCEYN, Ciudad Universitaria (1428), Buenos Aires, Argentina
Departamento de Matematicas, Universidad Autonoma de Madrid Crta, Colmenar Viejo km 15, 28049 Madridh, Spain
Instituto de Matematicas y Física Fundamental, Consejo Superior de Investigaciones Cientfficas, Serrano 123, Madrid, Spain
Departamento de Matematica, FCEyN UBA (1428), Buenos Aires, Argentina
Palabras clave:homogenization; nonlinear boundary conditions; Sobolev trace embedding.
Año:2008
Volumen:49
Número:2
Página de inicio:213
Página de fin:230
DOI: http://dx.doi.org/10.1017/S1446181100012797
Título revista:ANZIAM Journal
Título revista abreviado:ANZIAM J.
ISSN:14461811
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_14461811_v49_n2_p213_Fernandezbonder.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14461811_v49_n2_p213_Fernandezbonder

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Citas:

---------- APA ----------
Fernandezbonder, J., Orive, R. & Rossi, J.D. (2008) . The best Sobolev trace constant in domains with holes for critical or subcritical exponents. ANZIAM Journal, 49(2), 213-230.
http://dx.doi.org/10.1017/S1446181100012797
---------- CHICAGO ----------
Fernandezbonder, J., Orive, R., Rossi, J.D. "The best Sobolev trace constant in domains with holes for critical or subcritical exponents" . ANZIAM Journal 49, no. 2 (2008) : 213-230.
http://dx.doi.org/10.1017/S1446181100012797
---------- MLA ----------
Fernandezbonder, J., Orive, R., Rossi, J.D. "The best Sobolev trace constant in domains with holes for critical or subcritical exponents" . ANZIAM Journal, vol. 49, no. 2, 2008, pp. 213-230.
http://dx.doi.org/10.1017/S1446181100012797
---------- VANCOUVER ----------
Fernandezbonder, J., Orive, R., Rossi, J.D. The best Sobolev trace constant in domains with holes for critical or subcritical exponents. ANZIAM J. 2008;49(2):213-230.
http://dx.doi.org/10.1017/S1446181100012797