So here is the problem statement:

In addition, the following "hint" is given:Consider the equation

(6.12).

Let be a solution of (6.12) in each of two regions separated by a curve . Let be continuous, but have a jump discontinuity along the curve. Prove that

and hence that the curve is characteristic.

I believe denote the limits of from the right and left, respectively, and similarly for .Hint: By (6.12)

.

Moreover, and are continuous on the curve.

This is all from Fritz John'sPartial Differential Equations, exercise 1.6.3, p19.

I'm pretty lost on this one. Any help would be much appreciated. Thanks !