# A mean value theorem for the heat equation

```@inproceedings{Fulks1966AMV,
title={A mean value theorem for the heat equation},
author={Watson Fulks},
year={1966}
}```
The Gauss mean value theorem and its converse, due to Koebe, characterize solutions of Laplace's equation . In view of the strong analogy between Laplace's equation and the heat equation it seems reasonable to expect an analogue of the Gauss-Koebe result to hold for the heat equation. The purpose of this paper is to present such a result. For simplicity we work in two dimensions, though it is clear from the calculations that the result is independent of dimensions. Murakami  has used a…
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