On the heat content for the Poisson kernel over the unit ball in the euclidean space

Abstract

This paper studies, by employing analytical tools, the small-time behavior of the heat content for the Poisson kernel over the unit ball in R d , d ⩾ 2 by working with its related set covariance function. As a result, we obtain a representation for the third term in the expansion of the heat content over the unit ball and provide the explicit form of this term in the particular cases d = 2 and d = 3 .