Homogenization of the Ginzburg–Landau functional with a surface energy term

Article type: Research Article

Authors: Berlyand, Leonid

Affiliations: Department of Mathematics, Penn State University, University Park, PA 16802, USA E‐mail: berlyand@math.psu.edu

Abstract: We study a nonlinear homogenization problem in perforated domains for the Ginzburg–Landau functional with a surface energy integral term which was introduced in the theory of liquid crystals. Under certain conditions between the inclusion size and the order of the surface energy integral we compute the nonlinear homogenized problem and prove the convergence of the solutions. An additional relation between the domain size and physical parameters provides the uniqueness of the homogenized limit. Our proof is based on a variational approach and does not require strict periodicity of the perforated domains.

Keywords: Homogenization, Ginzburg–Landau functional, surface energy

Journal: Asymptotic Analysis, vol. 21, no. 1, pp. 37-59, 1999