Homogenization of Multiple Integrals

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9780198502463: Homogenization of Multiple Integrals

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. The structures under consideration may model cellular elastic materials, fibred materials, stratified or porous media, or materials with many holes or cracks. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents an introduction to the mathematical theory of homogenization of nonlinear integral functionals, with particular regard to those general results that do not rely on smoothness or convexity assumptions. Homogenization results and appropriate descriptive formulas are given for periodic and almost- periodic functionals. The applications include the asymptotic behaviour of oscillating energies describing cellular hyperelastic materials, porous media, materials with stiff and soft inclusions, fibered media, homogenization of HamiltonJacobi equations and Riemannian metrics, materials with multiple scales of microstructure and with multi-dimensional structure. The book includes a specifically designed, self-contained and up-to-date introduction to the relevant results of the direct methods of Gamma-convergence and of the theory of weak lower semicontinuous integral functionals depending on vector-valued functions. The book is based on various courses taught at the advanced graduate level. Prerequisites are a basic knowledge of Sobolev spaces, standard functional analysis and measure theory. The presentation is completed by several examples and exercises.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

  • 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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Braides, Andrea; Defranceschi, Anneliese
Editore: Cary, North Carolina, U.S.A.: Oxford Univ Pr on Demand (1999)
ISBN 10: 019850246X ISBN 13: 9780198502463
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Descrizione libro Cary, North Carolina, U.S.A.: Oxford Univ Pr on Demand, 1999. Hardcover. Condizione libro: New. Language: eng Language: eng Language: eng. Codice libro della libreria V41

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Braides, Andrea; Defranceschi, Anneliese
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Descrizione libro OUP Oxford, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780198502463_lsuk

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Descrizione libro Oxford University Press, USA, 1999. Hardcover. Condizione libro: New. Codice libro della libreria DADAX019850246X

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Braides, Andrea; Defranceschi, Anneliese
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Descrizione libro Clarendon Press, 1998. HRD. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780198502463

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Descrizione libro Clarendon Press, 1998. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Codice libro della libreria IP-9780198502463

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Descrizione libro Oxford University Press, United Kingdom, 1999. Hardback. Condizione libro: New. 236 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****.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. The structures under consideration may model cellular elastic materials, fibred materials, stratified or porous media, or materials with many holes or cracks. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents an introduction to the mathematical theory of homogenization of nonlinear integral functionals, with particular regard to those general results that do not rely on smoothness or convexity assumptions. Homogenization results and appropriate descriptive formulas are given for periodic and almost- periodic functionals. The applications include the asymptotic behaviour of oscillating energies describing cellular hyperelastic materials, porous media, materials with stiff and soft inclusions, fibered media, homogenization of HamiltonJacobi equations and Riemannian metrics, materials with multiple scales of microstructure and with multi-dimensional structure. The book includes a specifically designed, self-contained and up-to-date introduction to the relevant results of the direct methods of Gamma-convergence and of the theory of weak lower semicontinuous integral functionals depending on vector-valued functions. The book is based on various courses taught at the advanced graduate level. Prerequisites are a basic knowledge of Sobolev spaces, standard functional analysis and measure theory. The presentation is completed by several examples and exercises. Codice libro della libreria APC9780198502463

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Braides, Andrea; Defranceschi, Anneliese
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Descrizione libro Oxford University Press, United Kingdom, 1999. Hardback. Condizione libro: New. 236 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****. 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. The structures under consideration may model cellular elastic materials, fibred materials, stratified or porous media, or materials with many holes or cracks. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents an introduction to the mathematical theory of homogenization of nonlinear integral functionals, with particular regard to those general results that do not rely on smoothness or convexity assumptions. Homogenization results and appropriate descriptive formulas are given for periodic and almost- periodic functionals. The applications include the asymptotic behaviour of oscillating energies describing cellular hyperelastic materials, porous media, materials with stiff and soft inclusions, fibered media, homogenization of HamiltonJacobi equations and Riemannian metrics, materials with multiple scales of microstructure and with multi-dimensional structure. The book includes a specifically designed, self-contained and up-to-date introduction to the relevant results of the direct methods of Gamma-convergence and of the theory of weak lower semicontinuous integral functionals depending on vector-valued functions. The book is based on various courses taught at the advanced graduate level. Prerequisites are a basic knowledge of Sobolev spaces, standard functional analysis and measure theory. The presentation is completed by several examples and exercises. Codice libro della libreria APC9780198502463

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Descrizione libro Oxford Univ Pr on Demand, 1999. Hardcover. Condizione libro: Brand New. 1st ed, 1st pr edition. 312 pages. 9.75x6.50x0.75 inches. In Stock. Codice libro della libreria zk019850246X

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Descrizione libro OUP Oxford. Hardcover. Condizione libro: New. Hardcover. 312 pages. Dimensions: 9.3in. x 6.2in. x 1.0in.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 item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Codice libro della libreria 9780198502463

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Braides, Andrea; Defranceschi, Anneliese
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Descrizione libro Oxford University Press, 1999. Hardcover. Condizione libro: New. book. Codice libro della libreria 019850246X

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