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.
An Illustrated Guide of the Modern Approches of Hamilton-Jacobi Equations and Control Problems with Discontinuities
Approximation of functions on a compact set by solutions of elliptic equations. Quantitative results
A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source
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