Calculus of Variations and Geometric Measure Theory

N. Varchon

Optimal measures for nonlinear functionals

created on 26 Jul 2004


Submitted Paper

Inserted: 26 jul 2004

Journal: JOTA
Pages: 15
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 nonlinear. We prove a regularity result for the optimal measure, give a description of it and present some numerical examples.

Keywords: Gamma-convergence, shape optimization, measure theory