JournalszaaVol. 26 , No. 3DOI 10.4171/zaa/1324

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

Abstract

The homogenization of quadratic integral functionals for combined structures with singular or asymptotically singular reinforcement is studied in a model case in dimension N=2.N=2. Generalizations to more general cases in dimension N=2N=2 or to some model cases in dimension N>2N>2 are discussed. Such results are obtained in the frame of homogenization of problems depending on two parameters developed by V.~V.~Zhikov in %%% here alteration: citations have been expanded. [\textit{Funct. Anal. Appl.} 33 (1999)(1)], [\textit{Sb.~Math.} 191 (2000)(7-8)], and [{\it 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.