Introduction to Homogenization and Gamma-convergence
نویسنده
چکیده
These Lecture Notes contain the abstract of ve lectures conceived as an introduction to -convergence methods in the theory of Homogenization, and delivered on September 8{10, 1993 as part of the \School on Homogenization" at the ICTP, Trieste. Their content is strictly linked and complementary to the subject of the courses held at the same School by A. Defranceschi and G. Buttazzo. Prerequisites are some basic knowledge of functional analysis and of Sobolev spaces. An enlarged version of these Lecture Notes is contained in A. Braides and A. Defranceschi Homogenization of Multiple Integrals, Oxford University Press, Oxford, 1998
منابع مشابه
An Introduction to Homogenization and Gamma-convergence
CONTENTS 1. Γ-convergence for integral functionals. 2. A general compactness result. 3. Homogenization formulas. 4. Examples: homogenization without standard growth conditions. 5. Examples: other homogenization formulas. 43 44 Andrea Braides This paper contains the abstract of five lectures conceived as an introduction to Γ-convergence methods in the theory of Homogenization, and delivered on S...
متن کاملA Brief Introduction to Homogenization and Miscellaneous Applications
Abstract. This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of G− or H−convergence. Several applications of the method are given: derivation o...
متن کاملHomogenization and Two - Scale Convergence *
Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale" limit, up to a st...
متن کاملBloch Wave Homogenization of Linear Elasticity System
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a re...
متن کاملReview of Contemporary Homogenization Methods
We give some examples of existing mathematical methods for homogenizing partial differential equations (PDEs). In particular we will explore homogenization in Fourier space. The Maxwell equations are homogenized as an example of the method. INTRODUCTION Homogenization of PDEs is a mathematical method in which one find homogeneous material approximations of heterogeneous materials. That is, for ...
متن کامل