Heat content and Brownian motion for some regions with a fractal boundary |
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| Authors: | M. van den Berg |
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| Affiliation: | 1. Department of Mathematics, Heriot-Watt University, Riccarton, EH14 4AS, Edinburgh, UK
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| Abstract: | LetD be an open, bounded set in euclidean space  m (m=2, 3, ...) with boundary  D. SupposeD has temperature 0 at timet=0, while D is kept at temperature 1 for allt>0. We use brownian motion to obtain estimates for the solution of corresponding heat equation and to obtain results for the asymptotic behaviour ofED(t), the amount of heat inD at timet, ast 0+. For the triadic von Koch snowflakeK our results imply that
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