  We establish existence and uniqueness of minimax solutions for a fairly
general class of path-dependent Hamilton-Jacobi equations. In particular, the
relevant Hamiltonians can contain the solution and they only need to be
measurable with respect to time. We apply our results to optimal control
problems of (delay) functional differential equations with cost functionals
that have discount factors and with time-measurable data. Our main results are
also crucial for our companion paper Bandini and Keller (2024), where non-local
path-dependent Hamilton-Jacobi-Bellman equations associated to the stochastic
optimal control of non-Markovian piecewise deterministic processes are studied.
