Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions

作者：Luo Yousong^*

来源：Applied Mathematics and Optimization, 2010, 61(3): 337-351.

DOI：10.1007/s00245-009-9087-8

• Boundary control
• Optimality condition
• Elliptic equation
• Vettsel boundary condition

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.

• 出版日期2010-6