The author studies a variational problem on phase transition in continuum mechanics under the condition that the surface tension coefficient vanishes. The energy functional has the form \(I_0(u,\chi)=\int_\Omega\{\chi(F^+(\nabla u)+t)+ (1-\chi)F^-(\nabla u)+g\cdot u\}\,dx+\int_{\partial\Omega}f\cdot u\,dS,\;\) where \(F^\pm(\nabla u)=a_{ijkl}^\pm(u_{x_j}^i-\xi_{ij}^\pm)(u_{x_l}^k-\xi_{ij}^\pm)\) are elements of the tensor of elasticity moduli and \(\chi\) is the characteristic function. The domain of the functional is defined by formulas \(\mathbb X=\{u\in W^1_2(\Omega,\mathbb R^m),\;u|_\Gamma=u_0|_\Gamma\}\), \(\mathbb Z'=\{\chi\in L_\infty(\Omega)\), \(\chi^2(x)=\chi(x)\) a.e. in \(\Omega\}\), where \(\Gamma\subset \partial\Omega\) is a fixed subset of a positive measure, and a fixed function \(u_0\in W^1_2(\Omega,\mathbb R^m)\) determines the displacement field on \(\Gamma\).
An equilibrium displacement field \(\hat u\in\mathbb X\) and equilibrium phase distribution \(\hat \chi\in \mathbb Z'\) solve the variational problem \(I_0[\hat u,\hat\chi]=\inf_{u\in\mathbb X,\chi\in \mathbb Z'}I_0[u,\chi].\) After preliminary minimizing with respect to \(\chi\in\mathbb Z'\), the author solves the variational problem relative to an equilibrium displacement field \(I_{\min}[\hat u]=\inf_{u\in\mathbb X}I_{\min}[u]\) with not weakly lower semicontinuous functional \(I_{\min}\). It is shown that if a force field is nonzero almost everywhere, then the problem has only spherically symmetric solutions.