  In this paper, we discuss energy estimates for a particular class of linear
hyperbolic boundary value problems known as weakly regular of real type. Such
class, also called WR in the literature, is relevant in many physical
situations like the formation of shock waves in isentropic gas dynamics. In
this and other WR examples, the failure of the uniform Lopatinskii condition
plays a major role since it is associated with a loss of regularity in the
scale of Sobolev spaces, eventually leading to energy inequalities that are
ill-suited for nonlinear problems when solved by iteration. In the course of
this work, we derive a priori estimates for the model case that are comparable
to existing results, but using a more robust approach that we can extend to
scalar or system problems with variable coefficients. The result is a
significant step towards the ultimate goal of having estimates that can be
combined with Piccard's or Newton's iterative scheme to analyze nonlinear
situations.
