An existence result for a class of shape optimization problems
An existence result for a class of shape optimization problems
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一类形状优化问题的存在性结果
DOI：
10.1007/bf00378167
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发表时间：
1993
影响因子：
2.5
通讯作者：
G. Maso
中科院分区：
文献类型：
--
作者：
G. Buttazzo;G. Maso
给定一个Rn的有界开子集Ω，我们证明了在所有Ω的“拟开”子集的族a （Ω）上定义的泛函F的最小点的存在性，假设F相对于集合包含是递减的，并且F相对于a （Ω）上是下半连续的，这与具有Dirichlet边界条件的拉普拉斯算子的解有关。对给定椭圆算子，给出了具有最小第k个特征值（或最小容量）的规定体积集的存在性的应用。
Given a bounded open subset Ω of Rn, we prove the existence of a minimum point for a functional F defined on the family A(Ω) of all “quasiopen” subsets of Ω, under the assumption that F is decreasing with respect to set inclusion and that F is lower semicontinuous on A(Ω) with respect to a suitable topology, related to the resolvents of the Laplace operator with Dirichlet boundary condition. Applications are given to the existence of sets of prescribed volume with minimal kth eigenvalue (or with minimal capacity) with respect to a given elliptic operator.