[Author] Osmolovskii, V. G. [Title] Mathematical problems of the theory of phase transitions in a mechanics of continua [AMS Subj-class] 74N15 Analysis of microstructure 49J15 Methods involving semicontinuity and convergence; relaxation 35R35 Free boundary problems [Abstract] For one of possible macroscopic models of the theory of phase transitions in a mechanics of cotninua its mathematical examination is reduced. The special attention is given to stady to such physically important problems, as association of states of an equilibrium on temperature, coefficient of a surface-tension and domain occupied two-phase elastic medium. [Keywords] phase transitions, nonconvex variational problems, free boundary. [Comments] Russian, 123 pp. [Contact e-mail] vicos@VO8167.spb.edu