On homogenization for periodic elliptic second order differential operators in a strip
Nikita N. Senik · 2012
This paper concerns homogenization for the elliptic operator in L2(Π), Π = R × (0,a), defined by the differential expression Bλε= Σj=12Djgj(x1/ε, x2) Dj+ Σj=12(hj(x1/ε, x2) Dj+ Djhj*(x1/ε, x2)) + Q(x1/ε, x2) + λQ*(x1/ε, x2) with periodic, Neumann or Dirichlet boundary conditions. All the coefficients are assumed to be periodic of period 1 with respect to the first variable. Sharp-order approximations for the inverse of Bλε in the norms of B(L2(Π)) and B(L2(Π), H1(Π)) are obtained, with error terms being O(ε).