On existence of optimal controls in coecients for ill-posed nonlinear elliptic Dirichlet boundary value problems with anisotropic p-Laplacian

Abstract

We study a Dirichlet optimal control problem for a nonlinear elliptic anisotropic p-Laplace equation with control and state constraints. The matrix-valued coecients we take as controls and in the linear part of dierential operator we consider coecients to be unbounded skew-symmetric matrix. We show that, in spite of unboundedness of the non-linear dierential operator, the considered Dirichlet problem admits at least one weak solution and the corresponding OCP is well-possed and solvable.

Keywords

• optimal control
• anisotropic elliptic equation
• control in coefficients
• existence result