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 of H is the leading term in the asymptotic expansion of t ¿ Kt.
|Journal||Journal of the London Mathematical Society. Second Series|
|Publication status||Published - 2001|
Dungey, N., Elst, ter, A. F. M., & Robinson, D. W. (2001). On second-order almost-periodic elliptic operators. Journal of the London Mathematical Society. Second Series, 63(3), 735-753. https://doi.org/10.1017/S0024610701002149