Sufficient conditions for elliptic problem of optimal control in ²

(Lobachevskii Journal of Mathematics, Volume VI)

It is known that when we look for sufficient conditions of local extremum for Gateaux functionals (G.f) associated to Dirichlet problem of second order in ², the (G.f) is not necesseraly Frechet differentiable. In this note, using a recent extension of Frechet Differentiability, we obtain that the (G.f) is differentiable with respect to the new notion. Thus we can give sufficient conditions for obtaining local minimum.