On optimal control problem for nonlinear elliptic equation with variable p(x)-Laplacian

Abstract

An optimal control problem for the Dirichlet boundary value problem for the nonlinear elliptic equation with p(x)-Laplacian is considered. It is shown that this problem has at least one solution with respect to certain set of admissible pairs. The corresponding theoretic framework regarding Sobolev-Orlicz spaces is given.

Keywords

• nonlinear elliptic equation
• optimal control problem
• p(x)-Laplacian
• Lavrientiev phenomenon
• existence theorem