  This paper is concerned with inverse scattering problems of determining the
support of an isotropic and homogeneous penetrable body from knowledge of
multi-static far-field patterns in acoustics and in linear elasticity. The
normal derivative of the total fields admits no jump on the interface of the
scatterer in the trace sense. If the contrast function of the refractive index
function or the density function has a positive lower bound near the boundary,
we propose a hyper-singular source method to prove uniqueness of inverse
scattering with all incoming plane waves at a fixed energy. It is based on
subtle analysis on the leading part of the scattered field when hyper-singular
sources caused by the first derivative of the fundamental solution approach to
a boundary point. As a by-product, we show that this hyper-singular method can
be also used to determine the boundary value of a Holder continuous refractive
index function in acoustics or a Holder continuous density function in linear
elasticity.
