Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

Hambly, B. M.

Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 153-180

Résumé

We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpinski carpets. For all these functions the leading term is of the form $ {{x}^{\text{ }\!\!\gamma\!\!\text{ }}}\phi \left( \log x \right)$ for a suitable exponent $\text{ }\!\!\gamma\!\!\text{ }$ and $\phi $ a periodic function. We also discuss similar results for the heat content of affine nested fractals.

Détail

DOI : 10.4153/CJM-2010-079-7

Mots-clés : 35K05, 28A80, 35B40, 60J65

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