Journal article
ON SOME NONLOCAL VARIATIONAL PROBLEMS
- CHIPOT, MICHEL Institut für Mathematik, Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH–8057 Zürich, Switzerland
- GANGBO, WILFRID School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA
- KAWOHL, BERND Mathematisches Institut, Universität zu Köln, D 50923 Köln, Germany
- 2011-11-20
Published in:
- Analysis and Applications. - World Scientific Pub Co Pte Lt. - 2006, vol. 04, no. 04, p. 345-356
English
We study uniqueness and non uniqueness of minimizers of functionals involving nonlocal quantities. We give also conditions which lead to a lack of minimizers and we show how minimization on an infinite dimensional space reduces here to a minimization on ℝ. Among other things, we prove that uniqueness of minimizers of functionals of the form ∫Ω a(∫Ω gu dx)|∇u|2 dx - 2 ∫Ω fu dx is ensured if a > 0 and 1/a is strictly concave in the sense that (1/a)″ < 0 on (0, ∞).
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1142/s0219530506000814
- ISSN 0219-5305
- Persistent URL
- https://sonar.ch/global/documents/213069
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