Compactness of $M$-uniform domains and optimal thermal insulation problems

Abstract

In this paper, we will consider an optimal shape problem of heat insulation introduced by Bucur-Buttazzo-Nitsch. We will establish the existence of optimal shapes in the class of $M$-uniform domains. We will also show that balls are stable solutions of the optimal heat insulation problem.

32 pages

References in corpus (1)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces