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

. 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 \in W^{2,p}(\Omega) u ∈ W 2 , p ( Ω )

and the Lagrange multiplier

\overline \mu \in L^p(\Omega) μ ‾ ∈ L p ( Ω )

.