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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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MORE HOMOGENIZATION PROBLEMS

MORE HOMOGENIZATION PROBLEMS

Chapter:
(p.132) 9 MORE HOMOGENIZATION PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0010

This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two phenomena must be considered together. The first example deals with the interaction between oscillations and phase transitions in producing surface terms. The second exhibits a different scaling of the same problem giving a limit energy finite on piecewise-Sobolev functions through phase accumulation. The third example deals with the homogenization of free-discontinuity problems.

Keywords:   multiple-scale, interaction of scales, surface energies, free-discontinuity problems, phase accumulation

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