Calculus of Variations and Geometric Measure Theory

P. Acampora - E. Cristoforoni - C. Nitsch - C. Trombetti

A free boundary problem in thermal insulation with a prescribed heat source

created by acampora on 05 Jul 2024



Inserted: 5 jul 2024

Year: 2022

ArXiv: 2205.03275 PDF


We study the thermal insulation of a bounded body $\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a 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.