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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