Calculus of Variations and Geometric Measure Theory

G. Buttazzo - A. Nayam

Stationary Configuration of some Optimal Shaping

created by nayam on 13 May 2012
modified on 07 Sep 2013


Published Paper

Inserted: 13 may 2012
Last Updated: 7 sep 2013

Journal: International journal of dynamical system and differential equation
Volume: 4
Pages: 198-214
Year: 2012


Abstract: We consider the problem of optimal location of a Dirichlet region in a d-dimensional domain ­ subjected to a given right-hand side f in order to minimize some given functional of the configuration. While in the literature the Dirichlet region is usually taken d-1 dimensional, in this shape optimization 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.