科研之友
微信
新浪微博
Facebook
分享链接
摘要
In this paper we give a method to geometrically modify an open set such that the first k eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure remains constant, and both perimeter and diameter decrease below a certain threshold. The key point of the analysis relies on the properties of the shape subsolutions for the torsion energy. As well, we apply this result to prove existence of solutions for shape optimization problems of spectral type with both measure and perimeter constraints.
- 出版日期2015
