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

Giuseppe Cardone | Zendy; Antonio Esposito | Zendy; S. E. Pastukhova | Zendy

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

Author(s) -

Giuseppe Cardone,

Antonio Esposito,

S. E. Pastukhova

Publication year - 2007

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1324

Subject(s) - homogenization (climate) , reinforcement , mathematics , mathematical analysis , pure mathematics , materials science , composite material , biodiversity , ecology , biology

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. Generalizations to more general cases in dimension N = 2 or to some model cases in dimension N > 2 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.

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