Homogenization of p(x)-Laplacian in perforated domain swith a nonlocal transmission condition
2009 - B. Amaziane, L. Pankratov, V. Prytula
C. R. Mecanique 337, 173-178 (2009)
Abtract
We study the asymptotic behavior, as ε→0, of uε solutions to a nonlinear elliptic equation with nonstandard growth condition in domains containing a grid-type microstructure View the MathML source that is concentrated in an arbitrary small neighborhood of a given hypersurface Γ. We assume that uε=Aε on View the MathML source, where Aε is an unknown constant. The macroscopic equation and a nonlocal transmission condition on Γ are obtained by the variational homogenization technique in the framework of Sobolev spaces with variables exponents. This result is then illustrated by a periodic example.