Line-energy Ginzburg-Landau models : zero-energy states
Pierre-Emmanuel Jabin, Felix Otto, BenoÎt Perthame (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and...