Gamma-convergence for Beginners
By (author) Andrea Braides
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Gamma-convergence for Beginners by Andrea Braides
Book DescriptionThe 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 to Fracture 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 stimulating starting 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, where more 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 a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
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Book DetailsISBN: 9780198507840
(237mm x 157mm x 12mm)
Imprint: Clarendon Press
Publisher: Oxford University Press
Publish Date: 25-Jul-2002
Country of Publication: United Kingdom
Books By Author Andrea Braides
Homogenization of Multiple Integrals, Hardback (November 1998)» View all books by Andrea Braides
A rigorous mathematical description of the overall properties of fast-oscillating differential equations or integral functionals, which also includes an introduction to the theory of convergence and weak lower semicontinuous functionals. The text is volume number 12 in the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS.
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Author Biography - Andrea Braides
Prof. Andrea Braides Address Via Balilla 22, 00185 Roma, ITALY Tel (+39)0670452392 (home) (+39)0672594688 (office) Fax (+39)0672594699 Email email@example.com Italian, Udine (Italy), April 12,1961
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