
Homogenization theory describes the macroscopic properties of structures with fine microstructure. Its applications are diverse and include optimal design and the study of composites. The theory relies on the asymptotic analysis of fast-oscillating differential equations or integral functionals. This book is an introduction to the homogenization of nonlinear integral functionals. It emphasizes general results that do not rely on smoothness or convexity assumptions. 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. The book also includes self-contained introductions to the theories of gamma-convergence and weak lower semicontinuous functionals.
This book investigates the mathematical framework required to describe the macroscopic properties of structures characterized by fine, fast-oscillating microstructures. Andrea Braides and Anneliese Defranceschi provide a rigorous introduction to the homogenization of nonlinear integral functionals. By focusing on asymptotic analysis, the authors establish a methodology that remains effective even when traditional smoothness or convexity assumptions are absent. The text serves as a foundational reference for understanding how local variations in material properties aggregate into predictable global behaviors.
What You Will Find
Experts recognize this work as a foundational text for researchers and graduate students specializing in the calculus of variations and homogenization theory. Readers frequently note the technical density of the prose, which requires a strong background in functional analysis to fully grasp the presented proofs and applications.
Page Count:
312
Publication Date:
1999-02-18
Publisher:
Clarendon Press
ISBN-10:
019850246X
ISBN-13:
9780198502463
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