  In this paper we study a problem in radiotherapy treatment planning, where
the evolution of the radiation field is governed by a deterministic Boltzmann
transport equation. We show existence, uniqueness and regularity of solutions
to an optimal dose distribution problem constrained by the Boltzmann Continuous
Slowing-Down equation in an appropriate function space. The main new difficulty
is the treatment of the stopping power term. Furthermore, we characterize
optimal controls for problems governed by this transport equation.

Optimization and Control