SHARP BOUNDS ON HEAT KERNELS OF HIGHER ORDER UNIFORMLY ELLIPTIC OPERATORS

摘要

We consider uniformly elliptic operators of order 2m in diver-gence form with measurable coefficients'acting on domains in RN. The cor-responding heat kernel is known to satisfy bounds of the type. provided N < 2m. We use quadratic form techniques, semigroup theory and Sobolev inequalities to establish explicit sharp estimates for the constant C2. in terms of the ellipticity ratio of the operator.