##
*
A.Addou, S. Lahrech
*

Sufficient conditions for elliptic problem

of optimal control in $\R^2$

*(Lobachevskii Journal of Mathematics,
Vol.6, pp.3-17)*

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

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