%0 Journal Article
%T On the heat content of a polygon
%A Michiel van den Berg
%A Katie Gittins
%J Mathematics
%D 2015
%I arXiv
%X Let $D$ be a bounded, connected, open set in Euclidean space $\R^{2}$ 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 $t \downarrow 0$.
%U http://arxiv.org/abs/1504.04165v2