科研之友
微信
新浪微博
Facebook
分享链接
摘要
We establish an isoperimetric inequality with constraint by n-dimensional lattices. We prove that, among all sets which consist of lattice translations of a given rectangular parallelepiped, a cube is the best shape to minimize the ratio involving its perimeter and volume as long as the cube is realizable by the lattice. For its proof a solvability of finite difference Poisson-Neumann problems is verified. Our approach to the isoperimetric inequality is based on the technique used in a proof of the Aleksandrov-Bakelman-Pucci maximum principle, which was originally proposed by Cabr (Butll Soc Catalana Mat 15: 7-27, 2000) to prove the classical isoperimetric inequality.
- 出版日期2014-9
