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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Limiting models in condensed matter Physics and gradient flows of 1-homogeneous functional
verfasst von : Matteo Novaga, Giandomenico Orlandi
Erschienen in: Geometric Partial Differential Equations proceedings
Verlag: Scuola Normale Superiore
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We survey some recent results on variational and evolution problems concerning a certain class of convex 1-homogeneous functionals for vector-valued maps related to models in phase transitions (Hele-Shaw), superconductivity (Ginzburg-Landau) and superfluidity (Gross-Ktaevskii). Minimizers and gradient flows of such functionals may be characterized as solutions of suitable non-local vectorial generalizations of the classical obstacle problem.