Abstract
The existence of minimizers of a variational problem is investigated for the energy (not necessarily quasiconvex) functional of a two-phase elastic medium with classical energy densities in an arbitrary bounded domain. Some special boundary conditions are also considered. Bibliography: 6 titles.
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References
V. G. Osmolovskii, “Criterion for the lower semicontinuity of the energy functional of a two-phase elastic medium” [in Russian], Probl. Mat. Anal., 26, 215–254 (2003); English transl.: J. Math. Sci., 117 (2003), No. 3, 4211–4236.
V. G. Osmolovskii, Variational Problem on Phase Transitions in Mechanics of Continuous Media [in Russian], St.-Petersburg, St.-Petersburg Univ. Press (2000).
V. G. Maz'ya, Sobolev Spaces, Leningrad, Leningrad Univ. Press (1985).
A. S. Mikhailov and V. S. Mikhailov, “Remark on covering theorem” [in Russian], Probl. Mat. Anal., 24, 147–154 (2002); English transl.: J. Math. Sci., 112 (2002), No. 1, 4024–4028.
S. Müller, Microstructures, Phase Transitions and Geometry, Leipzig, Max-Planc-Institut (1997), Preprint No. 3.
Z. Hashin, “The elastic moduli of heterogeneuos materials,” J. Appl. Mech., 29 (1962), 143–159.
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Osmolovskii, V.G. Exact Solutions to the Variational Problem of the Phase Transition Theory in Continuum Mechanics. Journal of Mathematical Sciences 120, 1167–1190 (2004). https://doi.org/10.1023/B:JOTH.0000014845.60594.5f
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DOI: https://doi.org/10.1023/B:JOTH.0000014845.60594.5f