  In this paper, we study the problem of shock reflection by a wedge, with the
potential flow equation, which is a simplification of the Euler System.
  In the work of M. Feldman and G. Chen, the existence theory of shock
reflection problems with the potential flow equation was established, when the
wedge is symmetric w.r.t. the direction of the upstream flow. As a natural
extension, we study non-symmetric cases, i.e. when the direction of the
upstream flow forms a nonzero angle with the symmetry axis of the wedge.
  The main idea of investigating the existence of solutions to non-symmetric
problems is to study the symmetry of the solution. Then difficulties arise such
as free boundaries and degenerate ellipticity, especially when ellipticity
degenerates on the free boundary. We developed an integral method to overcome
these difficulties.
  Some estimates near the corner of wedge is also established, as an extension
of G.Lieberman's work.
  We proved that in non-symmetric cases, the ideal Lipschitz solution to the
potential flow equation, which we call regular solution, does not exist. This
suggests that the potential flow solutions to the non-symmetric shock
reflection problem, should have some singularity which is not encountered in
symmetric case.
