Processi di controllo con parametri distribuiti in insiemi non limitati. Insieme raggiungibile.

We study the attainable set for the following control process: z_{xy} + A(x,y)z_x +B(x,y)z_y + C(x,y)z = F(x,y) U(x,y) + G(x,x) a.e. (x,y) \in L(\alpha, \beta), where L(\alpha, \beta) = ([0,\alpha[ \times [0,+\infty[) \cup ([0,+\infty[ \times [0,\beta[), \alpha,\beta \in ]0,+\infty], the control U belongs to the space L^p_{loc}(L(\alpha, \beta), {\mathbb R}^m) and the final state, which is the trace of z on l(a,b)=([a,+\infty[\times\{b\})\cup\{\{a\}\times[b,+\infty[), (a,b) \in ]0,\alpha[\times]0,\beta[, belongs to a space of Sobolev type. We characterize the closed convex hull of the attainable set; also, we give some sufficient conditions in order that the attainable set may be closed (and convex). To this aim we previously establish some properties of the L^p_{loc} spaces.