| Автор | Pasquignon, Denis |
| Дата выпуска | 1999 |
| dc.description | We consider in $\mathbb{R}^2$ all curvature equation $\frac{\partial u}{\partial t}=|Du|G({\rm curv}(u))$ where G is a nondecreasing function and curv(u) is the curvature of the level line passing by x. These equations are invariant with respect to any contrast change u → g(u), with g nondecreasing. Consider the contrast invariant operator $T_t: u_o\to u(t)$. A Matheron theorem asserts that all contrast invariant operator T can be put in a form $(Tu)({\bf x}) = \inf_{B\in {\cal B}}\sup_{{\bf y}\in B} u({\bf x}+{\bf y})$. We show the asymptotic equivalence of both formulations. More precisely, we show that all curvature equations can be obtained as the iteration of Matheron operators $T_h^n$ where h → 0 and n → ∞ with nh=t. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 1999 |
| Тема | Viscosity solutions |
| Тема | inf-sup scheme |
| Тема | morphological filter. |
| Название | Approximation of viscosity solution by morphological filters |
| Тип | research-article |
| DOI | 10.1051/cocv:1999112 |
| Electronic ISSN | 1262-3377 |
| Print ISSN | 1292-8119 |
| Журнал | ESAIM: Control, Optimisation and Calculus of Variations |
| Том | 4 |
| Первая страница | 335 |
| Последняя страница | 359 |
| Аффилиация | Pasquignon Denis; CEREMADE, Université de Paris Dauphine, place de Lattre de Tassigny, 75775 Paris Cedex 16, France; pasquig@pi.ceremade.dauphine.fr. |
