\(\Gamma\)-limits of singular perturbation problems involving energies with non-local terms (Q1754668)
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scientific article; zbMATH DE number 6877193
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\Gamma\)-limits of singular perturbation problems involving energies with non-local terms |
scientific article; zbMATH DE number 6877193 |
Statements
\(\Gamma\)-limits of singular perturbation problems involving energies with non-local terms (English)
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31 May 2018
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The author introduces a new method to reformulate certain classes of problems involving non-local terms as local problems. This allows to apply the techniques developed for the \(\Gamma\)-limit of singular perturbation problems with optimal profiles which are not one-dimensional [the author, Differ. Integral Equ. 26, No. 9--10, 1179--1234 (2013; Zbl 1299.35046); Isr. J. Math. 210, 359--398 (2015; Zbl 1331.35028)], to prove upper and lower bounds for problems arising in micromagnetics and in the variational study of the Method of Vanishing Viscosity for systems of conservation laws.
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singular perturbation functional
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non-locality
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gradient theory
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