Calculus of Variations and Geometric Measure Theory

G. Buttazzo - N. Varchon - H. Zoubairi

Optimal measures for elliptic problems

created on 12 Mar 2004
modified on 26 Jul 2004


Accepted Paper

Inserted: 12 mar 2004
Last Updated: 26 jul 2004

Journal: Annali Mat. Pur. Appl.
Year: 2004


We study an optimization problem for an elliptic PDE where the unknown is a measure. The state equation is a relaxed form of the classical Dirichlet problem and the functional to minimize is the energy of the system. We prove a regularity result for the optimal measure, give a description of it and present some numerical examples.

Keywords: Gamma-convergence, optimization, measure