Estimates for low-frequency elastic scattering by a rigid body (Q582963)

The authors consider the following problem: Suppose we consider plane elastic waves scattered by a rigid body. It is known that the radial as well as the angular part of the scattering amplitude have leading low- frequency terms that are proportional to the integral of the traction field over the surface of the scatterer. Is it possible to find upper and lower bounds of this integral of the traction? The authors actually give two kinds of lower and upper bounds. One kind involves the capacity of the scatterer and the other one is based on the geometric characteristics of the scatterer. These bounds are sharp in the sense that they both become equalities when the scatterer reduces to an ellipsoid.