Stationary configuration of some optimal shaping

Abstract

We consider the problem of optimal location of a Dirichlet region in a d -dimensional domain Ω subjected to a given right-hand side f in order to minimise some given functional of the configuration. While in the literature the Dirichlet region is usually taken d – 1 dimensional, in this shape optimisation problems, we consider two classes of control variables, namely the class of one-dimensional closed connected sets of finite one-dimensional Hausdorff measure and the class of sets of points of finite cardinality, and we give a necessary condition of optimality.

Locations

• International Journal of Dynamical Systems and Differential Equations - View
• arXiv (Cornell University) - View - PDF