1 results
Upper bounds for a class of energies containinga non-local term
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 4 / October 2010
- Published online by Cambridge University Press:
- 31 July 2009, pp. 856-886
- Print publication:
- October 2010
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- Article
- Export citation
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In this paper we construct upper bounds for families offunctionals of the form
$$E_\varepsilon(\phi):=\int_\Omega\Big(\varepsilon |\nabla\phi|^2+\frac{1}{\varepsilon }W(\phi)\Big){\rm d}x+\frac{1}{\varepsilon }\int_{{\mathbb{R}}^N}|\nabla \bar H_{F(\phi)}|^2{\rm d}x$$
where Δ $\bar H_u$
= div { $\chi_\Omega$ 
u}. Particular cases of such functionals arise inMicromagnetics. We also use our technique to construct upper boundsfor functionals that appear in a variational formulation ofthe method of vanishing viscosity for conservation laws.
