Time: 9h30, Tuesday, July 28, 2020

Location: Room 612, Building A6, Institute of Mathematics

Abstract: We talk about second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is countably $PC^2$. We prove that the control-to-state operator is continuously differentiable although the nonlinear coefficient is non-smooth. This enables us to establish second-order necessary and sufficient optimality conditions. The ''gap'' between them is formulated in terms of jump discontinuity points of the derivative of the nonlinear coefficient. This gap will vanish if the nonlinear coefficient has a countably $PC^1$ derivative. A condition that is equivalent to the second-order sufficient optimality condition and could be useful for error estimates in, e.g., finite element discretization is also provided.