An Introduction To Estimates Of Heat Kernel And Dirichlet Heat Kernel

This paper summarizes the heat kernel estimate and Dirichlet heat kernel estimates of some local operators and non-local operators in finite dimensional Euclidean space.This introduction consists of two parts.The framework is as follows:In the first part,we mianly introduce estimates of heat kernel for some local oper-ators,non-local operators and fractional Laplacian operator with perturbation in finite dimensional Euclidean space.In the second part,we mianly introduce estimates of heat kernel for some local operators,non-local operators and fractional Laplacian operator with perturbation in some domains of finite dimensional Euclidean space.