Kinetic methods for Line–energy Ginzburg–Landau models
نویسنده
چکیده
A class of variational problems arising in thin micromagnetic film or in the gradient theory of phase transitions exhibit an hyperbolic behavior, a surprising property being given their natural elliptic structure. These two–dimensional Ginzburg–Landau problems are, for instance, characterized by energy density concentrations on a one–dimensional set comparable to a steady shock wave. Here we review how methods based on kinetic formulations can help to understand some feautures of this broad and fascinating class of problems. Especially we deduce a general regularity result and also we characterize the zero-energy states and the domains where they can occur.
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