HOMOGENIZATION OF VARIATIONAL FUNCTIONALS WITH NONSTANDARD GROWTH IN PERFORATED DOMAINS

The aim of the paper is to study the asymptotic behavior of solutions to a Neumann boundary value problem for a nonlinear elliptic equation with nonstandard growth condition of the form - div (vertical bar del u(epsilon)vertical bar(p epsilon(x)-2) del u(epsilon)) + vertical bar del u(epsilon)vertical bar(p epsilon(x)-2) u(epsilon) = f (x) in a perforated domain Omega(epsilon), epsilon being a small parameter that characterizes the microscopic length scale of the microstructure. Under the assumption that the functions p(epsilon)(x) converge uniformly to a limit function p(0)(x) and that p0 satisfy certain logarithmic uniform continuity condition, it is shown that u(epsilon) converges, as epsilon -> 0, to a solution of homogenized equation whose coefficients are calculated in terms of local energy characteristics of the domain Omega(epsilon). This result is then illustrated with periodic and locally periodic examples.