Determining the anisotropic traction state in a membrane by boundary measurements

where f(x) represents the distributed transverse load applied to it, and φ represents the prescribed transverse displacement at the boundary. In this note we wish to investigate the inverse problem of determining the plane traction state tensor σ from boundary measurements on displacements and on the corresponding forces. As an initial attempt, since the external load f has no influence on the pretraction state σ, and in analogy with many other well-known inverse boundary problems, see for instance [2, 8, 15], it seems natural to treat the case when f = 0 in (1.3), and consider as available data an arbitrary transverse displacement φ on the boundary and the corresponding transverse load on the boundary, namely the reaction of the boundary constraints