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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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*DIMENSION-REDUCTION PROBLEMS

*DIMENSION-REDUCTION PROBLEMS

Chapter:
(p.182) 14 *DIMENSION-REDUCTION PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0015

This chapter presents a brief treatment of problems defined on thin structures. A scaling argument allows the expression of the problem as an asymptotic study of degenerate energies on a single set. It is shown that the limit energy is independent on the ‘thin dimension’, and thus it is a dimensionally-reduced energy. In the convex case, the limit energy density is obtained by an optimization of a problem involving the original energy. An example shows that the same formula does not hold if the energies are polyconvex, and an additional quasiconvexification process is needed as in the theory of LeDret and Raoult.

Keywords:   thin domains, scaling argument, quasiconvexification, LeDret-Raoult

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