# 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.