Sufficient conditions for elliptic problem of optimal control in $\mathbb R^2$

A. Addou, S. Lahrech

Mohamed First University

Abstract: It is known that when we look for sufficient conditions of local extremum for Gâteaux functionals (G.f) associated to Dirichlet problem of second order in $\mathbb R^2$, the (G.f) is not necesseraly Frechet differentiable. In this note, using a recent extension of Frechet Differentiability, (see [5]), we obtain that the (G.f) is differentiable with respect to the new notion. Thus we can give sufficient conditions for obtaining local minimum.

Submitted by: A. V. Lapin
Received: 18.08.1999

Language: English

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