Upper bounds for a class of energies containing a non-local term
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, p. 856-886

In this paper we construct upper bounds for families of functionals of the form E ε (φ):= Ω ε|φ| 2 + 1 ε W (φ)dx+1 ε N |H ¯ F(φ) | 2 dx where Δ H ¯ u = div {χ Ω u}. Particular cases of such functionals arise in Micromagnetics. We also use our technique to construct upper bounds for functionals that appear in a variational formulation of the method of vanishing viscosity for conservation laws.

DOI : https://doi.org/10.1051/cocv/2009022
Classification:  35A15,  35J35,  82D40
Keywords: gamma-convergence, micromagnetics, non-local energy
@article{COCV_2010__16_4_856_0,
     author = {Poliakovsky, Arkady},
     title = {Upper bounds for a class of energies containing a non-local term},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     pages = {856-886},
     doi = {10.1051/cocv/2009022},
     zbl = {pre05821901},
     mrnumber = {2744154},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2010__16_4_856_0}
}
Poliakovsky, Arkady. Upper bounds for a class of energies containing a non-local term. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, pp. 856-886. doi : 10.1051/cocv/2009022. http://www.numdam.org/item/COCV_2010__16_4_856_0/

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