In this work we study, via $\Gamma$-convergence techniques, the asymptotic behaviour of a family of coupled singular perturbations of a non-convex functional of the type $$\int_\Omega f(u(x),\nabla u(x),\rho(x)) \, dx $$ as a variational model to address two-phase transitions problems under the volume constraints $\int_\Omega u(x)\, dx=V_f,$ $\int_\Omega \rho(x)\, dx =V_s,$ and where the additional unknown $\rho$ interplays with $\nabla u$ in the formation of interfaces. Joint work with: Ana Cristina Barroso and José Matias
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