95-357 Barbatis G., Davies E.B.

Sharp bounds on heat kernels of higher order uniformly elliptic operators. (40K, LaTeX) Jul 6, 95

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Abstract. We study higher order uniformly elliptic operators with measurable highest order coefficients acting on Euclidean domains. We obtain Gaussian heat kernel bounds for such operators and establish explicit estimates for the constant in the exponential term. These are expressed in terms of the ellipticity ratio of the operator and are sharp for powers of the Laplacian. We consider separately the case of homogeneous and non-homogeneous operators and distinguish between short- and long-time estimates. In each case, all our estimates are sharp in an appropriate asymptotic sense.

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