论文信息 - Regularity of solutions to a distributed and boundary optimal control problem governed by semilinear elliptic equations

Regularity of solutions to a distributed and boundary optimal control problem governed by semilinear elliptic equations

Abstract This paper deals with the existence and regularity of solutions to an optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints in which the controls act in the domain and on the boundary. We give some criteria under which the optimal solutions do exist and are Holder continuous.

Jen-Chih Yao | Ching-Feng Wen | Bui Trong Kien | Xiaolong Qin | Nguyen Thi Thu Huong

[1] V. H. Nhu,et al. Second-Order Optimality Conditions for a Semilinear Elliptic Optimal Control Problem with Mixed Pointwise Constraints , 2016, Set-Valued and Variational Analysis.

[2] E. Casas. Boundary control of semilinear elliptic equations with pointwise state constraints , 1993 .

[3] Fredi Tröltzsch,et al. Existence of Regular Lagrange Multipliers for a Nonlinear Elliptic Optimal Control Problem with Pointwise Control-State Constraints , 2006, SIAM J. Control. Optim..

[4] Fredi Tröltzsch,et al. On Regularity of Solutions and Lagrange Multipliers of Optimal Control Problems for Semilinear Equations with Mixed Pointwise Control-State Constraints , 2007, SIAM J. Control. Optim..

[5] Eduardo Casas,et al. Second Order Optimality Conditions for Semilinear Elliptic Control Problems with Finitely Many State Constraints , 2001, SIAM J. Control. Optim..

[6] Jen-Chih Yao,et al. Second-Order KKT Optimality Conditions for MultiObjective Optimal Control Problems , 2017, SIAM J. Control. Optim..

[7] Bui Trong Kien,et al. Second-Order Necessary Optimality Conditions for a Class of Semilinear Elliptic Optimal Control Problems with Mixed Pointwise Constraints , 2014, SIAM J. Control. Optim..