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 [2]. 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 [3] has used a… 
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