# The gradient theory of phase transitions and the minimal interface criterion

@article{Modica1987TheGT, title={The gradient theory of phase transitions and the minimal interface criterion}, author={L. Modica}, journal={Archive for Rational Mechanics and Analysis}, year={1987}, volume={98}, pages={123-142} }

In this paper I prove some conjectures of GURTIN [15] concerning the Van der Waals-Cahn-Hilliard theory of phase transitions. Consider a fluid, under isothermal conditions and confined to a bounded container 12 Q R', whose Gibbs free energy, per unit volume, is a prescribed function Wo of the density distribution u. The classical problem (cf. GURTIN [16]) of determining the stable configurations of the fluid is to minimize the total energy of the fluid, E(u) = f Wo(u(x)) dx, t2

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