Calculus of Variations and Geometric Measure Theory

G. Buttazzo - P. Guasoni

Shape Optimization Problems over Classes of Convex Domains

created on 15 Mar 1998
modified on 08 Feb 2001


Inserted: 15 mar 1998
Last Updated: 8 feb 2001

Journal: J. Convex Analysis
Number: 4-2
Pages: 1-9
Year: 1997


We consider shape optimization problems of the form \[ \min \left\{ \int_{\partial A} f(x,\nu(x)) d{\mathcal H}^{n-1}:\ A\in\mathcal{A}\right\} \] where $f$ is any continuous function and the class $\mathcal A$ of admissible domains is made of convex sets. We prove the existence of an optimal solution provided the domains satisfy some suitable constraints.