Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
复制标题
一维 Dirichlet 情况下 Ambrosio-Tortorelli 的临界点收敛于 Mumford-Shah 的临界点
DOI：
10.1051/cocv:2008041
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
S. Serfaty
中科院分区：
文献类型：
--
作者：
G. Francfort;N. Le;S. Serfaty
的Ambrosio-Tortorelli功能，非零Dirichlet边界条件取代的保真度项的变体的临界点进行了研究。他们被证明是con-verge特定的临界点的相应的变体的Mumford-Shah功能，这些表现出许多对称性。当处理弹性材料的脆性断裂问题时，狄利克雷变式是自然泛函。
Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to con- verge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.