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

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Abstract

In this paper we construct upper bounds for families of functionals of the form (Equation presented) where Δ Hu = div {χΩu}. 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.

Original languageEnglish
Pages (from-to)856-886
Number of pages31
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume16
Issue number4
DOIs
StatePublished - 1 Oct 2010
Externally publishedYes

Keywords

  • Gamma-convergence
  • Micromagnetics
  • Non-local energy

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