Processing math: 22%

MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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 (W10LM(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.

Creative Commons License

Keywords: Minimization problem, G\^ateaux functional, Orlicz-Sobolev space, uniformly elliptic operator, Frechet-differentiability, control problems.

MSC: 49K27

Pages:  37--49     

Volume  53 ,  Issue  1-2 ,  2001