This paper studies the small time behavior of the heat content for the Poisson kernel over a bounded open set $\dom\subset \Rd$, $d\geq 2$, of finite perimeter by working with the set covariance function. As a result, we obtain a third order expansion involving geometric features related to the underlying set $\dom$. We provide the explicit form of the third term for the unit ball when $d=2$ and $d=3$ and supply some results concerning the square $[-1,1]\times [-1,1]$. 查看全文>>