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 on a careful analysis of the corresponding weak solutions by the method of characteristics.
|Original language||English (US)|
|Number of pages||16|
|Journal||Annali della Scuola normale superiore di Pisa - Classe di scienze|
|State||Published - 2002|
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Mathematics (miscellaneous)