Chipot, M; Gangbo, W; Kawohl, B (2006). On some nonlocal variational problems. Analysis and Applications, 4(4):345-356.
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, ∞).
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, ∞).
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Uncontrolled Keywords: | Nonlocal, minimizer, calculus of variations |
| Language: | English |
| Date: | 2006 |
| Deposited On: | 07 Jan 2010 16:05 |
| Last Modified: | 03 Dec 2023 02:41 |
| Publisher: | World Scientific Publishing |
| ISSN: | 0219-5305 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1142/S0219530506000814 |
Chipot, M