Heat content and Brownian motion for some regions with a fractal boundary

M. van den Berg

Research output: Contribution to journalArticle

Abstract

Let D be an open, bounded set in euclidean space Rm (m=2, 3, ...) with boundary ?D. Suppose D has temperature 0 at time t=0, while ?D is kept at temperature 1 for all t>0. We use brownian motion to obtain estimates for the solution of corresponding heat equation and to obtain results for the asymptotic behaviour of ED(t), the amount of heat in D at time t, as t?0+. For the triadic von Koch snowflake K our results imply that {Mathematical expression} for some constant c>1. © 1994 Springer-Verlag.

Original languageEnglish
Pages (from-to)439-456
Number of pages18
JournalProbability Theory and Related Fields
Volume100
Issue number4
DOIs
Publication statusPublished - Dec 1994

Keywords

  • Mathematics Subject Classification: 60J45, 60J60, 60J65, 35K05

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