Optimal control of an elliptic equation with a nonsmooth nonlinearity (Q1778255)

The paper considers the problem of minimizing a quadratic functional on pairs \((y, u)\), which satisfy the elliptic equation \(\Delta y- g(y)= u+ f\) with the nondifferentiable function \(g\). Under assumptions of monotonicity of \(g\) the author approximates \(g\) by smooth functions, derives the optimality system for the approximate problem and shows the convergence of the corresponding costs of the approximate problems to the cost of the original problem.