ter Elst, A F M; Robinson, Derek; Sikora, Adam
We consider second-order, strongly elliptic, operators with complex coefficients in divergence form on Rd. We assume that the coefficients are all periodic with a common period. If the coefficients are continuous we derive Gaussian bounds, with the correct small and large time asymptotic behaviour, on the heat kernel and all its Hölder derivatives. Moreover, we show that the first-order Riesz transforms are bounded on the Lp-spaces with p ∈ (1, ∞). Secondly if the coefficients are Hölder...[Show more]
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