  Multi-wave inverse problems are indirect imaging methods using the
interaction of two different imaging modalities. One brings spatial accuracy,
and the other contrast sensitivity. The inversion method typically involve two
steps. The first step is devoted to accessing internal datum of quantities
related to the unknown parameters being observed. The second step involves
recovering the parameters themselves from the internal data. To perform that
inversion, a typical requirement is that the Jacobian of fields involved does
not vanish. A number of authors have considered this problem in the past two
decades, and a variety of methods have been developed. Existing techniques
require H{\"o}lder continuity of the parameters to be reconstructed. In
practical applications, the medium may present embedded elements, with distinct
physical properties, leading to discontinuous coefficients. In this article we
explain how a Jacobian constraint can imposed in the piecewise regular case,
when the physical model is a divergence form second order linear elliptic
boundary value problem.
