About classical solutions of the path-dependent heat equation

This paper investigates two existence theorems for the path-dependent heat equation, which is the Kolmogorov equation related to the window Brownian motion, considered as a C ([-T,0])} -valued process. We concentrate on two general existence results of its classical solutions related to different classes of terminal conditions: the first one is given by a cylindrical not necessarily smooth random variable, the second one is a smooth generic functional