Sufficient conditions for elliptic problem of optimal control in Rn in Orlicz Sobolev spaces

Authors

  • S. Lahrech Université Mohamed I, Faculté des Sciences, Département de Mathématiques et Informatique, Oujda, Maroc Author
  • A. Addou Université Mohamed I, Faculté des Sciences, Département de Mathématiques et Informatique, Oujda, Maroc Author

Keywords:

Minimization problem, Gâteaux functional, Orlicz-Sobolev space, uniformly elliptic operator, Frechet-differentiability, control problems

Subjects:

49K27

Abstract

This paper is concerned with the local minimization problem for a variety of non Frechet-differentiable Gâteaux functional J(f)ıntΩv(x,u,f)dx in the Orlicz-Sobolev space (W01LM(Ω),.M), 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.

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Published

2001-04-15