  The non-exponential Schilder-type theorem in Backhoff-Veraguas, Lacker and
Tangpi [Ann. Appl. Probab., 30 (2020), pp. 1321-1367] is expressed as a
convergence result for path-dependent partial differential equations with
appropriate notions of generalized solutions. This entails a non-Markovian
counterpart to the vanishing viscosity method.
  We show uniqueness of maximal subsolutions for path-dependent viscous
Hamilton-Jacobi equations related to convex super-quadratic backward stochastic
differential equations.
  We establish well-posedness for the Hamilton-Jacobi-Bellman equation
associated to a Bolza problem of the calculus of variations with path-dependent
terminal cost. In particular, uniqueness among lower semi-continuous solutions
holds and state constraints are admitted.
