Asymptotic behaviour of nonlinear problems in periodically perforated domains. The case p=N

Article type: Research Article

Authors: Casado‐Díaz, Juan

Affiliations: Dpto. de Ecuaciones diferenciales y Análisis Numérico, Universidad de Sevilla, Fac. de Matemáticas, C. Tarfía s/n, 41012 Sevilla, Spain E‐mail: jcasado@numer.us.es

Abstract: We present an extension of the two‐scale convergence method to the homogenization of monotone Dirichlet problems in periodically perforated domains, with critical size. The case of operators of order p strictly less than the dimension N of the space was considered in a previous paper. The case p=N presents several differences because it is a limit case for the Sobolev's imbedding theorem. Its study is the aim of this paper.

Journal: Asymptotic Analysis, vol. 30, no. 1, pp. 1-26, 2002