Calculus of Variations and Geometric Measure Theory

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

On the optimal shape of a thin insulating layer

created by acampora on 05 Jul 2024



Inserted: 5 jul 2024

Year: 2023

ArXiv: 2305.04078 PDF


We are interested in the thermal insulation of a bounded open set $\Omega$ surrounded by a set whose thickness is locally described by $\varepsilon h$, where $h$ is a non-negative function defined on the boundary $\partial\Omega$. We study the problem in the limit for $\varepsilon$ going to zero using a first-order asymptotic development by $\Gamma$-convergence.