  We study a control problem where the state equation is a nonlinear partial
differential equation of the calculus of variation in a bounded domain,
perturbed by noise. We allow the control to act on the boundary and set
stochastic boundary conditions that depend on the time derivative of the
solution on the boundary. This work provides necessary and sufficient
conditions of optimality in the form of a maximum principle. We also provide a
result of existence for the optimal control in the case where the control acts
linearly.
