Nonlocal effects in homogenization of \(p_\varepsilon (x)\)-Laplacian in perforated domains
The authors deal with the homogenization of a variational problem for a class of nonlinear elliptic equations of \(p_\varepsilon\)-Laplacian with non standard growth conditions. The considered domain has a connected inclusion like a net of infinitely high conductivity. The variational problem is studied in the framework of Sobolev spaces with variable exponents. The sequence of exponents \(p_\varepsilon\) are assumed as an oscillating continuous functions which converges in the uniform metric. The homogenized model, which induces nonlocal effects, is derived. The proof of this result is based on the variational homogenization technique and is illustrated with a periodic example in three dimensional space.
scientific article; zbMATH DE number 5577471
scientific article