Anatomy of the shape Hessian via lie brackets
Anatomy of the shape Hessian via lie brackets
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通过方括号解析 Hessian 形状
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Zolésio
中科院分区：
文献类型：
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作者：
D. Bucur;J. Zolésio
本文的目的是研究一类光滑泛函的形状Hessian的解剖。一个结构定理给出了作用于两个场的三种可加双线性形式的形状Hessian的分解：第一种形式作用于边界处的法向分量，第二种形式是对称的，第三种形式涉及计算形状Hessian的对场的李括号的一半。给出了结构定理中出现的混合导数的对易性和线性算子的对称性的应用。
The goal of this paper is to study the anatomy of the shape Hessian for some classes of smooth shape functionals. A structure theorem gives a decomposition of the shape Hessian in three additive bilinear forms acting on the two fields: the first one acting on the normal components at the boundary, the second one being symmetrical and the third one involving a half of the Lie bracket of the pair of fields at which the shape Hessian is computed. Applications to the commutation of the mixed derivatives and the symmetry of the linear operator which appears in the structure theorem are given.