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On the heat content of a polygon (1504.04165v3)
Published 16 Apr 2015 in math.AP
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 $t \downarrow 0$.