Correctors for some nonlinear monotone operators

• 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).

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

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Mathematics

Matematik

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