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

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

2009-04-07

arxiv.org/abs/0904.1060v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

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 constrain on the solution of the state equation is also considered.

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