Gamma-Convergence for Beginners by Andrea BraidesGamma-Convergence for Beginners by Andrea Braides

Gamma-Convergence for Beginners

byAndrea Braides

Hardcover | September 15, 2002

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The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing toFracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulatingstarting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals,then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, wheremore technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to anon-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
Prof. Andrea Braides Address Via Balilla 22, 00185 Roma, ITALY Tel (+39)0670452392 (home) (+39)0672594688 (office) Fax (+39)0672594699 Email Italian, Udine (Italy), April 12,1961
Title:Gamma-Convergence for BeginnersFormat:HardcoverDimensions:230 pages, 9.21 × 6.14 × 0.49 inPublished:September 15, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198507844

ISBN - 13:9780198507840

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Table of Contents

PrefaceIntroduction1. Gamma-convergence by numbers2. Integral problems3. Some homogenization problems4. From discrete systems to integral functionals5. Segmentation problems6. Phase-transition problems7. Free-discontinuity problems8. Approximation of free-discontinuity problems9. More homogenization problems10. Interaction between elliptic problems and partition problems11. Discrete systems and free-discontinuity problems12. *Some comments on vectorial problems13. *Dirichlet problems in perforated domains14. *Dimension-reduction problems15. *The 'slicing' method16. *An introduction to the localization method of Gamma-convergenceAppendicesA. Some quick recallsB. Characterization of Gamma-convergence for 1D(italic 'D') integral problemsList of symbolsReferencesIndex