ON SECOND-ORDER ALMOST-PERIODIC ELLIPTIC OPERATORS
Nick Dungey, A. F. M. ter Elst, Derek W. Robinson · Journal of the London Mathematical Society · 2001
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.