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Journal of Convex Analysis 25 (2018), No. 2, 529--543
Copyright Heldermann Verlag 2018

Radial Solutions and Free Boundary of the Elastic-Plastic Torsion Problem

Sofia Giuffrè
D.I.I.E.S., University of Reggio Calabria, Località Feo di Vito, 89122 Reggio Calabria, Italy

Aldo Pratelli
Department Mathematik, University of Erlangen, Cauerstr. 11, 91058 Erlangen, Germany

Daniele Puglisi
Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria 6, 95125 Catania, Italy


The paper is concerned with radial solutions to the elastic-plastic torsion problem, assuming the free term to belong to $L^p(\Omega)$. 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 $u \in W^{2,p}(\Omega)$ and the Lagrange multiplier $\overline \mu \in L^p(\Omega)$.

Keywords: Elastic-plastic torsion, radial solutions, Lagrange multipliers.

MSC: 35B06, 35R35

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