On two free boundary problems in potential theory
Lawrence Edward Payne, Gérard A. Philippin · Journal of Mathematical Analysis and Applications · 1991
In two dimensions, this problem plays a role in the theory of nonlinear elasticity, where the function u(x) may be interpreted as the stress function associated to an elasto-plastic beam of cross section Q c OX*. When g = 1, the problem reduces to that of the elastic torsion of a hollow cylinder, in which case our result is a natural extension of Serrin’s and Weinberger’s results [ 18, 193. The corresponding classical boundary value problem (i.e., with fixed &2 but