Fourier approach to homogenization problems
Departamento de Ingeniería
Matemática, and Centro de Modelamiento Matemático,
Universidad de Chile, Casilla 170/3, Correo-3, Santiago, Chile; firstname.lastname@example.org.
2 IISc-TIFR Mathematics Programme, TIFR Centre, P.O. Box 1234, Bangalore 560 012, India; email@example.com.
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic structures.
Mathematics Subject Classification: 35B27 / 35A25 / 42C30
Key words: Homogenization / Bloch waves / correctors / regularity / spectral problems / vibration problems.
© EDP Sciences, SMAI, 2002