We propose a notion of viscosity solutions for a class of fully nonlinear first-order path-dependent PDEs on Hilbert space. Under this notion, we prove uniqueness, existence, and stability for our equations. As an application, we study optimal control problems and differential games associated to nonlinear evolution equations with locally monotone and coercive operators, which were introduced by Liu (2011) and Liu and Rockner (2013). In particular, p-Laplace equations, 2D Navier-Stokes equations, tamed 3D Navier-Stokes equations, and power fluid laws can be dealt with in this framework. Currently, our theory has in its scope no counterpart in the non-path-dependent case.

Joint work with Erhan Bayraktar. Speaker(s): Christian Keller (UM)