An Optimization Problem in Heat Conduction With Volume Constraint and Double Obstacles

Xiaoliang Li, Cong Wang

We consider the optimization problem of minimizing ${\int }_{{\mathbb{R}}^n}|\nabla u{|}^2\mathrm{d}x$ with double obstacles $\varphi \le u\le \psi$ a.e. in $D$ and a constraint on the volume of…