Contingent and intermediate tangent cones in hyperbolic differential inclusions and necessary optimality conditions (Q1346359)

The author studies some properties of the contingent and intermediate cones to the reachable set of the differential inclusion \(u_{xy} \in F(x,y,u,u_ x,u_ y)\), with boundary conditions of the form \[ u(0,0) \in F_ 0, \;u_ x (x,0) \in F_ 1 \bigl( x,u(x,0) \bigr),\;u_ y(0,y) \in F_ 2 \bigl( y,u (0,y) \bigr). \] The above differential system is ``linearized'' by using techniques of nonsmooth analysis.