# Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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## The free boundary for elastic-plastic torsion problemsHTML articles powered by AMS MathViewer

by Avner Friedman and Gianni A. Pozzi
Trans. Amer. Math. Soc. 257 (1980), 411-425 Request permission

## Abstract:

Consider the variational inequality: Find $u \in K$ such that $\int _Q {\nabla u \cdot \nabla (\upsilon - u) \geqslant \mu \int _Q {(\upsilon - u) (\mu > 0)} }$ for any $\upsilon \in K$, where $K = \{ w \in H_0^1(Q); \left | {\nabla w} \right | \leqslant 1\}$ and Q is a 2-dimensional simply connected domain in ${R^2}$ with piecewise ${C^3}$ boundary. The solution u represents the stress function in a torsion problem of an elastic-plastic bar with cross section Q. The sets $E = \{ x \in Q; \left | {\nabla u(x)} \right | < 1\}$, $P = \{ x \in Q; \left | {\nabla u(x)} \right | = 1\}$ are the elastic and plastic sets respectively. The purpose of this paper is to study the free boundary $\partial E \cap Q$; more specifically, an estimate is derived on the number of points of local maximum of the free boundary.
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