A free boundary problem in thermal insulation with a prescribed heat source
Paolo Acampora, Emanuele Cristoforoni, Carlo Nitsch, Cristina Trombetti · ESAIM Control Optimisation and Calculus of Variations · 2022
We study the thermal insulation of a bounded body Ω G ℝn, under a prescribed heat sourcef> 0,viaa bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the environment determined by convection: this corresponds to Robin boundary conditions on the free boundary of the layer. We show that a minimal configuration exists and that it satisfies uniform density estimates.