Geodesic
The polarization in a ferroelectric thin film: local and nonlocal limit problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 657-667

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In this paper, starting from classical non-convex and nonlocal 3D-variational model of the electric polarization in a ferroelectric material, via an asymptotic process we obtain a rigorous 2D-variational model for a thin film. Depending on the initial boundary conditions, the limit problem can be either nonlocal or local.

DOI : 10.1051/cocv/2012026
Classification : 35Q61, 78A25
Keywords: electric polarization, thin film, nonlocal problems 
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     title = {The polarization in a ferroelectric thin film: local and nonlocal limit problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {657--667},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {3},
     year = {2013},
     doi = {10.1051/cocv/2012026},
     mrnumber = {3092355},
     zbl = {1291.35384},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012026/}
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Gaudiello, Antonio; Hamdache, Kamel. The polarization in a ferroelectric thin film: local and nonlocal limit problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 657-667. doi: 10.1051/cocv/2012026

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