It is shown that free energy functionals have a unique infinite-gradient limit which assures a finite interaction energy. This limit is used to extrapolate the Ginzburg-Landau small-gradient theory. The resulting functionals allow the existence of cusped equilibria or equilibria with sharp interfaces. If perturbed, a sharp interface will not quench immediately, but rather dissolve within a finite time.
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Philip Rosenau (1990) studied this question.