## Abstract

In this monograph we shall be concerned with a family of second-order linear elliptic operators in divergence form with rapidly oscillating periodic coefficients, Lε = -div A(x/ε)∇, ε>0, (2.0.1) in ℝ^{d}. The coefficient matrix (tensor) A in (2.0.1) is given by A(y) = a^{αβ} _{ij}(y), with 1 ≤ i, j ≤ d and 1 ≤ α, β ≤ m. Thus, if u = (u^{1}, u^{2}, …, u^{m}), [Formula Presented.] (the repeated indices are summed). We will always assume that A is real, bounded measurable, and satisfies a certain ellipticity condition, to be specified later. We also assume that A is 1-periodic; i.e., for each z ∈ ℤ^{d}, A(y + z) = A(y) for a.e. y ∈ ℝ^{d}. (2.0.2) Observe that by a linear transformation one may replace ℤ^{d} in (2.0.2) by any lattice in ℝ^{d}.

Original language | English |
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Title of host publication | Operator Theory |

Subtitle of host publication | Advances and Applications |

Pages | 7-31 |

Number of pages | 25 |

DOIs | |

State | Published - 2018 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 269 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Bibliographical note

Publisher Copyright:© Springer Nature Switzerland AG 2018.

## ASJC Scopus subject areas

- Analysis