Abstract
We study, via Γ-convergence, the asymptotic behavior of several classes of power–law functionals acting on fields belonging to variable exponent Lebesgue spaces and which are subject to constant rank differential constraints. Applications of the Γ-convergence results to the derivation and analysis of several models related to polycrystal plasticity arising as limiting cases of more flexible power–law models are also discussed.
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Communicated by L. Carbone.
The research of M. Bocea was partially supported by the US National Science Foundation under Grant No. DMS-0806789. M. Mihăilescu has been partially supported by Grant CNCSIS 79/2007 “Degenerate and Singular Nonlinear Processes”.
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Bocea, M., Mihăilescu, M. & Popovici, C. On the asymptotic behavior of variable exponent power–law functionals and applications. Ricerche mat. 59, 207–238 (2010). https://doi.org/10.1007/s11587-010-0081-x
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DOI: https://doi.org/10.1007/s11587-010-0081-x
Keywords
- \({\mathcal{A}}\) -quasiconvexity
- Γ-convergence
- Power–law functionals
- Variable exponent Lebesgue spaces
- Yield set