Glasnik Matematicki, Vol. 42, No.2 (2007), 375-388.

QUASILINEAR DIRICHLET PROBLEM IN A PERIODICALLY PERFORATED DOMAIN

L. Boukrim, A. Hakim and T. Mekkaoui

Université Moulay Ismail, F.S.T.E, BP509 Boutalamine Errachidia, Maroc

Université Cadi Ayyad, F.S.T.G, BP 549 Av. Abdelkrim Khattabi Marrakech, Maroc

Université Moulay Ismail, F.S.T.E, BP509 Boutalamine Errachidia, Maroc


Abstract.   Consider the following quasilinear Dirichlet problem (Pε)

    -Δp uε = fε     in   Ωε = Ω \ Tε
uε = 0     on   ∂ Ωε

where 1 < p ≤ 2, (fε) a sequence of functions in Lp'(Ω) such that fεf in Lp'(Ω) where p' is the conjugate of p, Ω is a bounded domain in RN (N ≥ 2) and Tε the union of inclusions contained in Ω which are ε-periodically distributed. In this paper we give the limit problem and errors estimates for the problem (Pε).

2000 Mathematics Subject Classification.   35B27, 35B40, 35J60.

Key words and phrases.   Homogenization, perforated domain, quasilinear elliptic equations, correctors.


Full text (PDF) (free access)

DOI: 10.3336/gm.42.2.11


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