A note on Young measures and correctors in $\Gamma$-convergence and homogenization
Author:
Pablo Pedregal
Journal:
Quart. Appl. Math. 68 (2010), 661-669
MSC (2010):
Primary 35B27, 49J45, 74Q05
DOI:
https://doi.org/10.1090/S0033-569X-2010-01184-8
Published electronically:
September 3, 2010
MathSciNet review:
2761509
Full-text PDF Free Access
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Additional Information
Abstract: We explore a general strategy to determine the Young measure associated with sequences of pairs of conductivity coefficients and corresponding gradient fields. We also relate this issue to corrector results and investigate various examples.
References
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- Pablo Pedregal, Young measures associated with homogenization, SIAM J. Math. Anal. 37 (2006), no. 5, 1454–1464. MR 2215272, DOI https://doi.org/10.1137/040614578
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References
- Allaire, G. Shape optimization by the homogenization method, 2002, Springer. MR 1859696 (2002h:49001)
- Balder, E. J. (2000), Lectures on Young measure theory and its applications in economics, in: Proceedings Grado School on Measure Theory and Real Analysis, Rend. Sem. Matem. Trieste 31, suppl. 1, 1–69. MR 1798830 (2001m:49069)
- Briane, M., Correctors for the homogenization of a laminate, Adv. Math. Sci. Appl., Gakk. Tokyo, 4, n. 2 (1994), 357–379. MR 1294225 (95h:35023)
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- Pankov, A., $G$-convergence and homogenization of nonlinear partial differential operators, Mathematics and its Applications, 422. Kluwer Academic Publishers, Dordrecht, 1997. MR 1482803 (99a:35017)
- Pedregal, P. (1997), Parametrized Measures and Variational Principles, Birkhäuser, Basel. MR 1452107 (98e:49001)
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- Pedregal, P., Young measures associated with homogenization, SIAM J. Math. Anal., 37, n. 5 (2006), 1454-1464. MR 2215272 (2006m:49023)
- Serrano, H., Ph.D. Thesis, U. Complutense, 2007.
- Valadier M. (1990), Young measures, Methods of Nonconvex Analysis, Lect. Notes in Math., 1446, Springer, 152-188. MR 1079763 (91j:28006)
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Additional Information
Pablo Pedregal
Affiliation:
Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
Email:
pablo.pedregal@uclm.es
Received by editor(s):
February 13, 2009
Published electronically:
September 3, 2010
Additional Notes:
Supported by project MTM2007-62945 (MEC, Spain) and by project PCI08-0084-0424 from JCCM (Castilla-La Mancha).
Article copyright:
© Copyright 2010
Brown University
The copyright for this article reverts to public domain 28 years after publication.