Abstract
We investigate the asymptotic behaviour of the heat content as the time t→ 0 for an s-adic von Koch snowflake generated by a square. We show that the heat content satisfies a functional equation which, after appropriate transformations, takes the form of an inhomogeneous renewal equation. We obtain the structure of the solution of this equation in the arithmetic case up to an exponentially small remainder in t. <!-ID=""Mathematics Subject Classification (2000): 35K05, 60J65, 28A80--> <!-ID=""Key words: Heat equation – Arithmetic – Snowflake-->
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 24 March 1999 / Revised version: 14 October 1999 / Published online : 8 August 2000
Rights and permissions
About this article
Cite this article
van den Berg, M. Heat equation on the arithmetic von Koch snowflake. Probab Theory Relat Fields 118, 17–36 (2000). https://doi.org/10.1007/PL00008740
Published:
Issue Date:
DOI: https://doi.org/10.1007/PL00008740