- Title Pages
- Dedication
- PREFACE
- INTRODUCTION
-
1 Γ-CONVERGENCE BY NUMBERS -
2 INTEGRAL PROBLEMS -
3 SOME HOMOGENIZATION PROBLEMS -
4 FROM DISCRETE SYSTEMS TO INTEGRAL FUNCTIONALS -
5 SEGMENTATION PROBLEMS -
6 PHASE-TRANSITION PROBLEMS -
7 FREE-DISCONTINUITY PROBLEMS -
8 APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS -
9 MORE HOMOGENIZATION PROBLEMS -
10 INTERACTION BETWEEN ELLIPTIC PROBLEMS AND PARTITION PROBLEMS -
11 DISCRETE SYSTEMS AND FREE-DISCONTINUITY PROBLEMS -
12 *SOME COMMENTS ON VECTORIAL PROBLEMS -
13 *DIRICHLET PROBLEMS IN PERFORATED DOMAINS -
14 *DIMENSION-REDUCTION PROBLEMS -
15 *THE ‘SLICING’ METHOD -
16 *AN INTRODUCTION TO THE LOCALIZATION METHOD OF Γ-CONVERGENCE -
APPENDIX A SOME QUICK RECALLS -
APPENDIX B CHARACTERIZATION OF Γ-CONVERGENCE FOR 1D INTEGRAL PROBLEMS - LIST OF SYMBOLS
- REFERENCES
- INDEX
SOME HOMOGENIZATION PROBLEMS
SOME HOMOGENIZATION PROBLEMS
- Chapter:
- (p.63) 3 SOME HOMOGENIZATION PROBLEMS
- Source:
- Gamma-Convergence for Beginners
- Author(s):
Andrea Braides
- Publisher:
- Oxford University Press
Homogenization problems for a general class of integrals are solved by a direct approach. Different homogenization formulas are given, both in an asymptotic form and as a cell problem (in the convex case). These are applied in the study of the asymptotic behaviour of Riemannian metrics and Hamilton-Jacobi equations.
Keywords: oscillating functionals, homogenization of integral functionals, homogenization formulas, Riemannian metrics, Hamilton-Jacobi equations
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- Title Pages
- Dedication
- PREFACE
- INTRODUCTION
-
1 Γ-CONVERGENCE BY NUMBERS -
2 INTEGRAL PROBLEMS -
3 SOME HOMOGENIZATION PROBLEMS -
4 FROM DISCRETE SYSTEMS TO INTEGRAL FUNCTIONALS -
5 SEGMENTATION PROBLEMS -
6 PHASE-TRANSITION PROBLEMS -
7 FREE-DISCONTINUITY PROBLEMS -
8 APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS -
9 MORE HOMOGENIZATION PROBLEMS -
10 INTERACTION BETWEEN ELLIPTIC PROBLEMS AND PARTITION PROBLEMS -
11 DISCRETE SYSTEMS AND FREE-DISCONTINUITY PROBLEMS -
12 *SOME COMMENTS ON VECTORIAL PROBLEMS -
13 *DIRICHLET PROBLEMS IN PERFORATED DOMAINS -
14 *DIMENSION-REDUCTION PROBLEMS -
15 *THE ‘SLICING’ METHOD -
16 *AN INTRODUCTION TO THE LOCALIZATION METHOD OF Γ-CONVERGENCE -
APPENDIX A SOME QUICK RECALLS -
APPENDIX B CHARACTERIZATION OF Γ-CONVERGENCE FOR 1D INTEGRAL PROBLEMS - LIST OF SYMBOLS
- REFERENCES
- INDEX
