## Communications in Mathematical Analysis

### Reiterated Homogenization of Linear Eigenvalue Problems in Multiscale Perforated Domains Beyond the Periodic Setting

#### Abstract

Reiterated homogenization of linear elliptic Neuman eigenvalue problems in multiscale perforated domains is considered beyond the periodic setting. The classical periodicity hypothesis on the coefficients of the operator is here substituted on each microscale by an abstract hypothesis covering a large set of concrete behaviors such as the periodicity, the almost periodicity, the weakly almost periodicity and many more besides. Furthermore, the usual double periodicity is generalized by considering a type of structure where the perforations on each scale follow not only the periodic distribution but also more complicated but realistic ones. Our main tool is Nguetseng's Sigma convergence.

#### Article information

Source
Commun. Math. Anal., Volume 11, Number 1 (2011), 61-93.

Dates
First available in Project Euclid: 22 December 2010

https://projecteuclid.org/euclid.cma/1293054275

Mathematical Reviews number (MathSciNet)
MR2753680

Zentralblatt MATH identifier
1206.35030

Subjects
Primary: 35B40
Secondary: 45C05 46J10

#### Citation

Douanla, Hermann; Svanstedt, Nils. Reiterated Homogenization of Linear Eigenvalue Problems in Multiscale Perforated Domains Beyond the Periodic Setting. Commun. Math. Anal. 11 (2011), no. 1, 61--93. https://projecteuclid.org/euclid.cma/1293054275