Multitime optimal control with area integral costs on boundary

This paper joins some concepts that appear in Mechanics, Field Theory, Differential Geometry and Control Theory in order to solve multitime optimal control problems with area integral costs on boundary. Section 1 recalls the multitime maximum principle in the sense of the first author. The main results in Section 2 include the needle-shaped control variations, the adjoint PDEs, the behavior of infinitesimal deformations and other ingredients needed for the multitime maximum principle in case of no running cost and in case of running cost. Section 3 solves the previous multitime control problems based on techniques of variational calculus. Section 4 shows that concavity is a sufficient condition in multitime optimal control theory. Section 5 contains an example illustrating the utility of such a multitime optimal control theory. M.S.C. 2010: 49J20, 49J40, 70H06, 37J35.