Non-existence of strong regular reflections in self-similar potential flow

We consider shock reflection which has a well-known local non-uniqueness: the reflected shock can be either of two choices, called weak and strong. We consider cases where existence of a global solution with weak reflected shock has been proven, for compressible potential flow. If there was a global strong-shock solution as well, then potential flow would be ill-posed. However, we prove non-existence of strong-shock analogues in a natural class of candidates.