Homogenization of Multiple Integrals

图书简介

The object of homogenization theory is the description of the macroscopic properties of structures with fine microstructure, covering a wide range of applications that run from the study of properties of composites to optimal design. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents a rigorous mathematical description of the overall properties of such functionals, with various applications that range from cellular elastic materials to Riemannian metrics and Hamilton-Jacobi equations. It includes a self-contained, specifically designed introduction to the theory of Gamma-convergence and weak lower semicontinuous functionals.

Preface; Contents; Introduction; Notation; Part I: Lower Semicontinuity; 1 Lower semicontinuity and coerciveness; 2 Weak convergence; 3 Minimum problems in sobolev spaces; 4 Necessary conditions for weak lower semicontinuity; 5 Sufficient conditions for weak lower semicontinuity; Part II: Gamma-convergence; 6 The structure of quasiconvex functions; 7 A naive introduction of Gamma-convergence; 8 The indirect methods of Gamma-convergence; 9 Direct methods - an integral representation result; 10 Increasing set functions; 11 The fundamental estimate; 12 Integral functionals with standard growth condition; Part III: Basic Homogenization; 13 A one-dimensional example; 14 Periodic homogenization; 15 Almost periodic homogenization; 16 Two applications; 17 A closure theorem for the homogenization; 18 Loss of polyconvexity by homogenization; Part IV: Finer Homogenization Results; 19 Homogenization of connected media; 20 Homogenization with stiff and soft inclusions; 21 Homogenization with non-standard growth conditions; 22 Iterated homogenization; 23 Correctors for the homogenization; 24 Homogenization of multi-dimensional structures; Part V: Appendices; A Almost periodic functions; B Construction of extension operators; C Some regularity results; References; Index

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Homogenization of Multiple Integrals（Oxford Lecture Series in Mathematics and Its Applications） 数学史

Homogenization of Multiple Integrals（Oxford Lecture Series in Mathematics and Its Applications）
数学史