Homogenization of the elliptic Dirichlet problem: operator error estimates in L₂

الأصل · EN

Let O ⊂ Rᵈ be a bounded domain of class C². In the Hilbert space L₂(O;Cⁿ), we consider a matrix elliptic second order differential operator AD,ε with the Dirichlet boundary condition. Here ε>0 is the small parameter. The coefficients of the operator are periodic and depend on x/ε. A sharp order operator error estimate AD,ε⁻¹ - (AD⁰)⁻¹ ₗ₂ → ₗ₂ ≤ C ε is obtained. Here A⁰D is the effective operator with constant coefficients and with the Dirichlet boundary condition.