We consider optimal control problems governed by semilinear elliptic equations with pointwise constraints on the state variable. The main difference with previous papers is that we consider nonlinear boundary conditions, elliptic operators with discontinuous leading coefficients and unbounded controls. We can deal with problems with integral control constraints and the control may be a coefficient of order zero in the equation. We derive optimality conditions by means of a new Lagrange multiplier theorem in Banach spaces.
Publié le : 1997-07-04
Classification:
Optimal control,
nonlinear boundary control,
optimality conditions,
Lagrange multipliers in Banach spaces,
pointwise state constraints,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00993905,
author = {Alibert, Jean-Jacques and Raymond, Jean-Pierre},
title = {Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls},
journal = {HAL},
volume = {1997},
number = {0},
year = {1997},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00993905}
}
Alibert, Jean-Jacques; Raymond, Jean-Pierre. Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls. HAL, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/hal-00993905/