Homogenization of Scalar Problem for a Combined Structure with Singular or Thin Reinforcement

  • Giuseppe Cardone

    Università del Sannio, Benevento, Italy
  • A. Corbo Esposito

    Università degli Studi di Cassino, Italy
  • S.E. Pastukhova

    Technical University, Moscow, Russian Federation

Abstract

The homogenization of quadratic integral functionals for combined structures with singular or asymptotically singular reinforcement is studied in a model case in dimension Generalizations to more general cases in dimension or to some model cases in dimension are discussed.

Such results are obtained in the frame of homogenization of problems depending on two parameters developed by V. V. Zhikov in [Funct. Anal. Appl. 33 (1999)(1)], [Sb. Math. 191 (2000)(7-8)], and [Izv. Math. 66 (2002)(2)]. In particular, an essential tool is the notion of two-scale convergence of sequences of functions belonging to Sobolev spaces with respect to variable measures.

Cite this article

Giuseppe Cardone, A. Corbo Esposito, S.E. Pastukhova, Homogenization of Scalar Problem for a Combined Structure with Singular or Thin Reinforcement. Z. Anal. Anwend. 26 (2007), no. 3, pp. 277–301

DOI 10.4171/ZAA/1324