Heat Kernel Bounds and Homogenization of Elliptic Operators
James R. Norris · Bulletin of the London Mathematical Society · 1994
We obtain upper and lower bounds on the heat kernel of a uniformly elliptic operator in divergence form with measurable coefficients. From these bounds one can deduce not only the familiar short-time asymptotics of the heat kernel, but in the case of periodic coefficients, long-time asymptotics involving homogenization of the coefficients.