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arXiv · 1407.6139

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

Michiel van den Berg·Katie Gittins
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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.

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Michiel van den Berg, Katie Gittins. 2016-07-29. Uniform bounds for the heat content of open sets in Euclidean space. https://doi.org/10.1016/j.difgeo.2015.01.010

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