On the heat content of a polygon

Abstract

Let $D$ be a bounded, connected, open set in Euclidean space ${\mathbb{R}}^2$ with polygonal boundary. Suppose $D$ has initial temperature $1$ and the complement of $D$ has initial temperature $0$. We obtain the asymptotic behaviour of the heat content of $D$ as time $t\downarrow 0$. We then apply this result to compute the heat content of a particular fractal polyhedron as $t\downarrow 0$.

23 pages, 1 figure

Cited by in corpus (1)

• On the heat content for the poisson kernels over the unit ball in the euclidean space