Abstract
Homogenization theory is concerned with the derivation of equations for averages of solutions of equations with rapidly varying coefficients. This problem arises in obtaining macroscopic, or `homogenized' of `effective', equations for systems with a fine microscopic structure. Our goal is to represent a complex, rapidly-varying medium by a slowly-varying medium in which the fine-scale structure is averaged out in an appropriate way.
We will consider the homogenization of second-order linear elliptic PDEs. This is a fundamental and physically important example, but similar ideas apply to many other types of linear and nonlinear PDEs, such as Hamilton--Jacobi equations and various kinds of time-dependent PDEs.
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