Lagrange multipliers in elastic–plastic torsion problem for nonlinear monotone operators

The existence of Lagrange multipliers as a Radon measure is ensured for an elastic–plastic torsion problem associated to a nonlinear strictly monotone operator. A regularization of this result, namely the existence of L^p Lagrange multipliers, is obtained under strong monotonicity assumption on the operator. Moreover, the relationships between elastic–plastic torsion problem and the obstacle problem are investigated. Finally, an example of the so-called “Von Mises functions” is provided, namely of solutions of the elastic–plastic torsion problem, associated to nonlinear monotone operators, which are not obtained by means of the obstacle problem in the case f=constant.