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Lagrange multipliers in elastic-plastic torsion problem for nonlinear monotone operators. (English) Zbl 1319.35258

Summary: 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 \(f = \text{constant}\).

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
65K10 Numerical optimization and variational techniques
49N15 Duality theory (optimization)
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