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Publication ahead of print
Issue ESAIM: COCV
DOI 10.1051/cocv/2009022
Published online 31 July 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009022

Upper bounds for a class of energies containing a non-local term

Arkady Poliakovsky

Fachbereich Mathematik, Universität Duisburg-Essen, Lotharstrasse 65, 47057 Duisburg, Germany. arkady.poliakovsky@math.uzh.ch


Received July 11, 2008. Published online July 31, 2009.

Abstract
In this paper we construct upper bounds for families of functionals of the form $ E_\varepsilon(\phi):=\int_\Omega\Big(\varepsilon\vert\nabla\phi\vert^2+\frac{\varepsilon}\int_{\mathbb\vert\nabla \bar H_{F(\phi)}\vert^2{\rm d}x $ where $\Delta \bar H_u = div\,\{\chi_\Omega u\}$. 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.


Mathematics Subject Classification. 35A15, 35J35, 82D40

Key words: Gamma-convergence, micromagnetics, non-local energy


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