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ON SECOND-ORDER ALMOST-PERIODIC ELLIPTIC OPERATORS

Published online by Cambridge University Press:  05 July 2001

N. DUNGEY ,
A. F. M. TER ELST  and
DEREK W. ROBINSON
N. DUNGEY
Affiliation:
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia
A. F. M. TER ELST
Affiliation:
Department of Mathematics and Computing Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, Netherlands
DEREK W. ROBINSON
Affiliation:
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia
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Abstract

The paper considers second-order, strongly elliptic, operators H with complex almost-periodic coefficients in divergence form on Rd. First, it is proved that the corresponding heat kernel is Hölder continuous and Gaussian bounds are derived with the correct small and large time asymptotic behaviour on the kernel and its Hölder derivatives. Secondly, it is established that the kernel has a variety of properties of almost-periodicity. Thirdly, it is demonstrated that the kernel of the homogenization Ĥ of H is the leading term in the asymptotic expansion of t [map ] Kt.

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Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 735 - 753
Copyright
The London Mathematical Society 2001

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