Prof. Carlo Nitsch “Shape optimization in a thermal insulation problem”

We study a shape optimization problem involving a solid K of R^n
which has constant temperature and it is surrounded by a layer of
insulating material Ω which obeys a generalized boundary heat transfer
law.
We minimize the energy of such configurations among all (K,Ω) with
prescribed measure for K and Ω, and without topological or
geometrical constraints.
In the convection case (corresponding to Robin boundary conditions
on ∂Ω) we obtain a full description of minimizers. In the general case,
we prove the existence and regularity of solutions and we give a partial
description of minimizers.