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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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INTERACTION BETWEEN ELLIPTIC PROBLEMS AND PARTITION PROBLEMS

INTERACTION BETWEEN ELLIPTIC PROBLEMS AND PARTITION PROBLEMS

Chapter:
(p.139) 10 INTERACTION BETWEEN ELLIPTIC PROBLEMS AND PARTITION PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0011

This chapter introduces the one-dimensional version of problems defined on functions of bounded variations. It is shown that for general energies, the surface and volume terms of the energy can interact, giving some compatibility conditions between the corresponding energy densities expressed through their recession functions. For these energies, relaxation results are given in terms of inf-convolution and convexification formulas that simplify in the case of convex and concave energies. Links with the theory of Structured Deformations are given.

Keywords:   bounded variation, surface and volume energies, recession function, inf-convolution, concave energies, structured deformations

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