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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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PHASE-TRANSITION PROBLEMS

PHASE-TRANSITION PROBLEMS

Chapter:
(p.102) 6 PHASE-TRANSITION PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0007

Phase transitions with sharp interfaces are interpreted as segmentation problems, and are approximated with perturbations of non-convex energies (gradient theory of phase transitions). The Modica-Mortola theorem is proved, with different formulas characterizing the segmentation energy (optimal-profile problems).

Keywords:   phase transitions, gradient theory, Modica-Mortola theorem, optimal-profile problem

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