We will study the inverse scattering problem for the Navier equation in elasticity with live loads. We give the definition of a Born approximation of the load from backscattering data. We will see that in 2D, for non-smooth load matrices the main singularities of the matrices are in fact contained in their Born approximations. The singularities are measured in the scale of Sobolev spaces.

In a two-dimensional plane problem of the theory elasticity in polar coordinates for nonhomogeneous body, it is possible to obtain analytical or numerical-analytical solutions only one-dimensional nonuniformity [1 - 3]. As rule, this when all unknown functions depend on radius. These tasks correspond majority ring and cylindrical structures exposed axisymmetric effects temperature, radiation, h...

In this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed nonconforming finite element methods: Implementation, postprocessing error estimates, ESAIM Math. Model. Numer. Anal. 19 (1985) 7–32] to Virtual Element Method for linear elasticity problems based on Hellinger–Reissner principle. To illustrate such a technique, focus specific 2D scheme, but other...