Upper bounds for a class of energies containing a non-local term
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 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∫ ℝ 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 : 10.1051/cocv/2009022
Classification : 35A15, 35J35, 82D40
Mots-clés : gamma-convergence, micromagnetics, non-local energy 
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Poliakovsky, Arkady. Upper bounds for a class of energies containing a non-local term. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 856-886. doi : 10.1051/cocv/2009022. http://www.numdam.org/articles/10.1051/cocv/2009022/

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