Nonlocal effects in homogenization of pε(x)pε(x)-Laplacian in perforated domains

We study the homogenization of a variational problem corresponding to a class of nonlinear elliptic equations with nonstandard growth in a domain with a connected inclusion like a net of infinitely high conductivity. The variational problem is studied in the framework of Sobolev spaces with variable exponents. We assume that the sequence of exponents, pε(x)pε(x), is an oscillating continuous functions which converges in the uniform metric. Then by means of the variational homogenization technique, we derive the homogenized model which induces nonlocal effects. This result is then illustrated with a periodic example in three space dimensions (3D).