| Автор | Dambrine, Marc |
| Автор | Pierre, Michel |
| Дата выпуска | 2000 |
| dc.description | We discuss the stability of "critical" or "equilibrium" shapes of a shape-dependent energy functional. We analyze a problem arising when looking at the positivity of the second derivative in order to prove that a critical shape is an optimal shape. Indeed, often when positivity -or coercivity- holds, it does for a weaker norm than the norm for which the functional is twice differentiable and local optimality cannot be a priori deduced. We solve this problem for a particular but significant example. We prove "weak-coercivity" of the second derivative uniformly in a "strong" neighborhood of the equilibrium shape. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 2000 |
| Тема | Shape optimisation |
| Тема | stability of critical shape |
| Тема | weak coercivity |
| Тема | area-preserving transformations. |
| Название | About stability of equilibrium shapes |
| Тип | research-article |
| DOI | 10.1051/m2an:2000105 |
| Electronic ISSN | 1290-3841 |
| Print ISSN | 0764-583X |
| Журнал | ESAIM: Mathematical Modelling and Numerical Analysis |
| Том | 34 |
| Первая страница | 811 |
| Последняя страница | 834 |
| Аффилиация | Dambrine Marc; Antenne de Bretagne de l'ENS Cachan, Institut de Recherche Mathématique de Rennes, Campus de Ker Lann, 35170 Bruz, France. (dambrine@bretagne.ens-cachan.fr) |
| Аффилиация | Pierre Michel; Antenne de Bretagne de l'ENS Cachan, Institut de Recherche Mathématique de Rennes, Campus de Ker Lann, 35170 Bruz, France. (pierre@bretagne.ens-cachan.fr) |
| Выпуск | 4 |
