Radial solutions and free boundary of the elastic-plastic torsion problem

The paper is concerned with radial solutions to the elastic-plastic torsion problem, assuming the free term to belong to L^p(Ω). In particular, we obtain a necessary and sufficient condition in order that the plastic region exists and we characterize the free boundary. Moreover, we find the explicit radial solution u ∈ W^{2,p}(Ω) and the Lagrange multiplier μ ∈ L^p(Ω).