Abstract
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.
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Novaga, M., Orlandi, G. (2013). Limiting models in condensed matter Physics and gradient flows of 1-homogeneous functional. In: Chambolle, A., Novaga, M., Valdinoci, E. (eds) Geometric Partial Differential Equations proceedings. CRM Series, vol 15. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-473-1_11
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DOI: https://doi.org/10.1007/978-88-7642-473-1_11
Publisher Name: Edizioni della Normale, Pisa
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