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.

DVI format (69Kb), ZIP-ed DVI format (20Kb),
ZIP-ed PostScript format (65Kb)