An Introduction to G-Convergence
1st Edition
Published on 1. January 1993
Book
Hardback
XIV, 341 pages
978-0-8176-3679-1 (ISBN)
Description
The last twentyfive years have seen an increasing interest for variational convergences and for their applications to different fields, like homogenization theory, phase transitions, singular perturbations, boundary value problems in wildly perturbed domains, approximation of variatonal problems, and non- smooth analysis. Among variational convergences, De Giorgi's r-convergence plays a cen- tral role for its compactness properties and for the large number of results concerning r -limits of integral functionals. Moreover, almost all other varia- tional convergences can be easily expressed in the language of r -convergence. This text originates from the notes of the courses on r -convergence held by the author in Trieste at the International School for Advanced Studies (S. I. S. S. A. ) during the academic years 1983-84,1986-87, 1990-91, and in Rome at the Istituto Nazionale di Alta Matematica (I. N. D. A. M. ) during the spring of 1987. This text is far from being a treatise on r -convergence and its appli- cations.
More details
Series
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Illustrations
XIV, 341 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 25 mm
Weight
705 gr
ISBN-13
978-0-8176-3679-1 (9780817636791)
DOI
10.1007/978-1-4612-0327-8
Schweitzer Classification
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An Introduction to G-Convergence
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An Introduction to G-Convergence
Book
12/1993
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Content
1. The direct method in the calculus of variations.- 2. Minimum problems for integral functionals.- 3. Relaxation.- 4. ?-convergence and K-convergence.- 5. Comparison with pointwise convergence.- 6. Some properties of ?-limits.- 7. Convergence of minima and of minimizers.- 8. Sequential characterization of ?-limits.- 9. ?-convergence in metric spaces.- 10. The topology of ?-convergence.- 11. ?-convergence in topological vector spaces.- 12. Quadratic forms and linear operators.- 13. Convergence of resolvents and G-convergence.- 14. Increasing set functions.- 15. Lower semicontinuous increasing functionals.- 16. $$ \bar{\Gamma } $$-convergence of increasing set functional.- 17. The topology of $$ \bar{\Gamma } $$-convergence.- 18. The fundamental estimate.- 19. Local functionals and the fundamental estimate.- 20. Integral representation of ?-limits.- 21. Boundary conditions.- 22. G-convergence of elliptic operators.- 23. Translation invariant functional.- 24. Homogenization.- 25. Some examples in homogenization.- Guide to the literature.