PHASE-TRANSITION WITH A POTENTIAL DEGENER ATED AT INFINITY, APPLICATION TO DROPLETS EQUILIBRIUM

In order to modelize the equilibrium of very small drops, we study the asymptotic behaviour as epsilon tends to 0 of the minimizers of: (P-e psilon inf{integral(0)(1) W(u(x)) + epsilon u'(2) (x) dx, integral(0)( 1) u dx = M}. The function W is non negative, vanishes only at u(0) ep silon R and satisfies lim(t-->+infinity W(t)/t = 0. In the limit confi guration, the mass distribution contains an atomic measure which corre sponds to droplets.