Correctors for some nonlinear monotone operators
2001 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 8, no 1, 8-30 p.Article in journal (Refereed) Published
In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/εh,Duh)) = fh on Ω with Dirichlet boundary conditions. Here the sequence (εh) tends to 0 as h→∞ and the map a (x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions.W e prove that uh → u weakly in W1,p 0 (Ω) as h → ∞, where u is the solution of a homogenized problem of the form -div (b (x,Du)) = f on Ω. We also derive an explicit expression for the homogenized operator b and prove some corrector results, i.e. we find (Ph) such that Duh -Ph (Du) → 0 in Lp (Ω,Rn). () 0 in (Ω).
Place, publisher, year, edition, pages
2001. Vol. 8, no 1, 8-30 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-12987DOI: 10.2991/jnmp.2001.8.1.2Local ID: c237de60-9e82-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-12987DiVA: diva2:985938
Validerad; 2001; 20070107 (ysko)2016-09-292016-09-29Bibliographically approved