Geodesic
A Nonlocal Problem Arising in the Study of Magneto-Elastic Interactions
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 197-221

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The energy of magneto-elastic materials is described by a nonconvex functional. Three terms of the total free energy are taken into account: the exchange energy, the elastic energy and the magneto-elastic energy usually adopted for cubic crystals. We focus our attention to a one dimensional penalty problem and study the gradient flow of the associated type Ginzburg-Landau functional. We prove the existence and uniqueness of a classical solution which tends asymptotically for subsequences to a stationary point of the energy functional. 
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     author = {Chipot, M. and Shafrir, I. and Vergara Caffarelli, G.},
     title = {A {Nonlocal} {Problem} {Arising} in the {Study} of {Magneto-Elastic} {Interactions}},
     journal = {Bollettino della Unione matematica italiana},
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Chipot, M.; Shafrir, I.; Vergara Caffarelli, G. A Nonlocal Problem Arising in the Study of Magneto-Elastic Interactions. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 197-221. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_1_a7/