Uniform bounds for the heat content of open sets in Euclidean space

Abstract

We obtain (i) lower and upper bounds for the heat content of an open set in ${\mathbb{R}}^m$ with $R$-smooth boundary and finite Lebesgue measure, (ii) a necessary and sufficient geometric condition for finiteness of the heat content in ${\mathbb{R}}^m$, and corresponding lower and upper bounds, (iii) lower and upper bounds for the heat loss of an open set in ${\mathbb{R}}^m$ with finite Lebesgue measure.

15 pages. The coefficient $h_3$ has been corrected in this version

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