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Gamma-Convergence for Beginners$
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Andrea Braides

Print publication date: 2002

Print ISBN-13: 9780198507840

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198507840.001.0001

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Gamma-Convergence for Beginners

Andrea Braides

Oxford University Press

This chapter introduces the space of piecewise-Sobolev functions, which is the one-dimensional version of the De Giorgi-Ambrosio SBV space. Sample applications to Signal Reconstruction (the Mumford-Shah functional) and Fracture Mechanics (Griffith fracture energy) are given. The Ambrosio compactness theorem is proved, and the necessary conditions are given for free-discontinuity energies. Existence results are derived.

Keywords:   piecewise-Sobolev functions, SBV spaces, signal reconstruction, fracture mechanics, Mumford-Shah functional, Griffith energy, free-discontinuity problems

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