Sufficient conditions for elliptic problem of optimal control in Rn
in Orlicz Sobolev spaces
S. Lahrech and A. Addou
Abstract
This paper is concerned with the local minimization problem for a
variety of non Frechet-differentiable G\^ateaux functional
J(f)≡∫Ωv(x,u,f)dx in the Orlicz-Sobolev space
(W10L∗M(Ω),‖, where u is the solution of
the Dirichlet problem for a linear uniformly elliptic
operator with nonhomogenous term f and \|.\|_{M} is
the Orlicz norm associated with an N-function~M.
We use a recent extension of Frechet-differentiability
(approach of Taylor mappings see [2]), and we give
various assumptions on v to guarantee a critical point is
a strict local minimum.
Finally, we give an example of a control problem where classical Frechet
differentiability cannot be used and their approach of Taylor mappings works.