  We consider differentiability issues associated to the problem of minimizing
the accumulation of a granular cohesionless material on a certain surface. The
design variable or control is determined by source locations and intensity
thereof. The control problem is described by an optimization problem in
function space and constrained by a variational inequality or a non-smooth
equation. We address a regularization approach via a family of nonlinear
partial differential equations, and provide a novel result of Newton
differentiability of the control-to-state map. Further, we discuss solution
algorithms for the state equation as well as for the optimization problem.
