Geodesic
Radial Solutions and Free Boundary of the Elastic-Plastic Torsion Problem
Journal of convex analysis, Tome 25 (2018) no. 2, pp. 529-543
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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 $\overline \mu \in L^p(\Omega)$.
Classification : 35B06, 35R35
Mots-clés : Elastic-plastic torsion, radial solutions, Lagrange multipliers 
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     author = {S. Giuffr\`e and A. Pratelli and D. Puglisi},
     title = {Radial {Solutions} and {Free} {Boundary} of the {Elastic-Plastic} {Torsion} {Problem}},
     journal = {Journal of convex analysis},
     pages = {529--543},
     year = {2018},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a10/}
}
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S. Giuffrè; A. Pratelli; D. Puglisi. Radial Solutions and Free Boundary of the Elastic-Plastic Torsion Problem. Journal of convex analysis, Tome 25 (2018) no. 2, pp. 529-543. http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a10/