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Sharp lower bounds for vector Allen-Cahn energy and qualitative properties of minimizes under no symmetry hypotheses
Nicholas D. Alikakos, Giorgio Fusco
We study vector minimizers u of the Allen-Cahn functional with potentials possessing N global minima defined on bounded domains, with certain geometrical features and Dirichlet con…
Minimizing under relaxed symmetry constraints: Triple and -junctions
Giorgio Fusco
We consider a nonnegative potential invariant under the action of the rotation group of the regular polygon with sides, . W…
Periodic motions for multi-wells potentials and layers dynamic for the vector Allen-Cahn equation
Giorgio Fusco
We consider a nonnegative potential that vanishes on a finite set and study the existence of periodic orbits of the equation \[\ddot{u}=W_u(u),\;\;t\in\R,\] that have the prope…
A replacement lemma for obtaining pointwise estimates in phase transition models
Nicholas D. Alikakos, Giorgio Fusco
We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.