The best Sobolev trace constant in domains with holes for critical or subcritical exponents

• Autores: Julián Fernández Bonder, Rafael Orive Illera , Julio Daniel Rossi
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 49, Nº 2, 2007, págs. 213-230
• Idioma: inglés
• DOI: 10.1017/s1446181100012797
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• Resumen

  • In this paper we study the best constant in the Sobolev trace embedding H1()Lq() in a bounded smooth domain for 1q2=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.