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Research Report MRR00-002
On second-order almost-periodic elliptic operators
N. Dungey, A.F.M. ter Elst and Derek W. Robinson
Abstract:
We consider second-order, strongly elliptic, operators
H with complex almost-periodic coefficients in divergence form
on Rd. First, we prove that the corresponding
heat kernel
is Hölder continuous and we derive Gaussian bounds with the
correct small and large time asymptotic behaviour on the kernel
and its Hölder derivatives. Secondly, we establish that the
kernel has a variety of properties of almost-periodicity. Thirdly,
we demonstrate that the kernel of the homogenization $\widehat H$
of H is the leading term in the asymptotic expansion of
t->Kt.
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