Stationary configuration of some optimal shaping
by Giuseppe Buttazzo; Al-hassem Nayam
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 4, No. 3, 2012

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.

Online publication date: Thu, 18-Oct-2012

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