HOẠT ĐỘNG TRONG TUẦN

Second-order optimality conditions of a quasilinear elliptic control problem with a non-smooth coefficient
Báo cáo viên: Vũ Hữu Nhự

Thời gian: 9h30 Thứ Ba ngày 28/7/2020

Địa điểm: 612 A6 Viện Toán học, 18B Hoàng Quốc Việt

Tóm tắt: 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.

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