Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state
The authors consider an optimal control problem of semilinear elliptic equations subject to control constraints and pointwise constraints on the gradient of the state. The control is distributed and assumed to belong to \(L^ r(\Omega)\) for some \(r>n\), thus allowing not to choose the control space among Sobolev spaces. So the main results obtained in the paper are: optimality conditions with more general state constraints and simpler Lagrange multiplier than in previous papers; regularity results; a detailed study of the adjoint state equation.
scientific article; zbMATH DE number 147399
scientific article