Title: Stationary configuration of some optimal shaping

Authors: Giuseppe Buttazzo; Al-hassem Nayam

Addresses: Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy. ' International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

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.

Keywords: shape optimisation; p-Laplacian; higher co-dimension; necessary conditions; optimality; stationary configuration; optimal shaping; Hausdorff measure; finite cardinality.

DOI: 10.1504/IJDSDE.2012.049886

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.3, pp.198 - 214

Published online: 18 Oct 2012 *

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