Affiliations: Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, and Centro de Modelamiento Matemático, UMR 2071 CNRS‐UChile, Casilla 170/3 – Correo 3, Santiago, Chile E‐mail: cconca@dim.uchile.cl | Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, España E‐mail: rafael.orive@uam.es | IISc‐TIFR Mathematics Programme, TIFR Center, P.O. Box 1234, Bangalore 560012, India E‐mail: vanni@math.tifrbng.res.in
Note: [] Corresponding author.
Abstract: The classical problem of homogenization deals with elliptic operators in periodically oscillating media of small period ε>0 and the asymptotic behavior of solution uε of boundary value problems associated with such operators. In a previous work [Conca et al., SIAM J. Math. Anal. 33 (2002), 1166–1198], the authors introduced what is called Bloch approximation which provided energy norm approximation for the solution in $\mathbb{R}^{N}$. This paper continues with the above development and proposes a modified Bloch approximation. This function takes into account boundary effects. Its connection with the first order classical correctors is also established with the corresponding error estimate. All the proofs are worked out entirely in the Fourier–Bloch space.
