Optimal coefficients for elliptic PDEs

Abstract

We consider an optimization problem related to elliptic PDEs of the form $-\mathrm{div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\hat{I}\text{c◯}$. The coefficient $a(x)$ has to be determined, in a suitable given class of admissible choices, in order to optimize a given criterion. We first deal with the case when the cost is the so-called elastic compliance, and then we discuss the more general case when the problem is written as an optimal control problem.

15 pages, 9 figures