Journal of Mathematical Sciences

, Volume 144, Issue 6, pp 4645–4654 | Cite as

On the set of solutions to a variational phase transition problem of continuum mechanics

  • V. G. Osmolovskii


A variational problem describing phase transitions is considered. It is shown that a multi-vaued function associating with the set of parameters the set of solutions to the problem is continuous and has compact values. Bibliography: 5 titles.


Phase Transition Equilibrium State Variational Problem Weak Convergence Strong Convergence 
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  1. 1.
    M. A. Grinfel’d, Methods of Continuum Mechanics in the Theory of Phase Transitions [in Russian], Moscow, Nauka, 1990.Google Scholar
  2. 2.
    V. G. Osmolovskii, “An existence theorem and weak Lagrange equations for a variational problem of the theory of phase transitions” [in Russian], Sib. Mat. Zhurn. 35 (1994), no. 4, 835–846; English transl: Sib. Math. J., 35 (1994), no. 4, 743–753.CrossRefGoogle Scholar
  3. 3.
    V. G. Osmolovskii, “Criterion for the lower semicontinuity of the energy functional of a two-phase elastic medium” [in Russian], Probl. Mat. Anal. 26 (2003), 215–254; English transl.: J. Math. Sci. New York 117 (2003), No. 3, 4211–4236.zbMATHGoogle Scholar
  4. 4.
    L.C. Evans, R.F. Gariepi, Measure Theory and Fine Properties of Functions, CRC Press. Boca Raton, 1992zbMATHGoogle Scholar
  5. 5.
    L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, Am. Math. Soc., 1990.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • V. G. Osmolovskii
    • 1
  1. 1.St.Petersburg State UniversityRussia

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