Prof. Cristina Trombetti “An optimization problem in thermal insulation”

We study thermal insulating of a bounded body. Under a prescribed
heat source, we consider a model of heat transfer between the body
and the environment determined by convection; this corresponds,
before insulation, to Robin boundary conditions. We study the
maximization of heat content (which measures the goodness of the
insulation) among all the possible distributions of insulating material with
fixed mass, and prove an optimal upper bound in terms of geometric
quantities. Eventually we prove a conjecture which states that the ball
surrounded by a uniform distribution of insulating material maximizes the heat content.

Joint work with: Francesco della Pietra (University of Naples Federico II),
Carlo Nitsch (University of Naples Federico II), Riccardo Scala (University of Siena).