On optimal controls in coefficients for ill-posed elliptic Neumann boundary value problem with anisotropic p-Laplace operator - Kogut, Peter; Kupenko, Olha (Nonlinear differential equations and applications, 2025)
We study an optimal control problem for a nonlinear elliptic anisotropic p-Laplace equation with control constraints and Neumann boundary conditions. The matrix-valued coefficients Asym∈L∞(Ω;SsymN) we take as controls and in the linear part of differential operator we consider coefficients to be unbounded skew-symmetric matrix Askew∈Lq(Ω;SskewN). We show that, in spite of unboundedness of the differential operator, the considered Neumann problem admits at least one weak solution and the corresponding OCP is well-possed and solvable.