In this talk I will present our result on the linear stability of contact discontinuities that separate C^1 supersonic flow from static gas, governed by the three dimensional steady non-isentropic compressible Euler equations. The linear problem is a one-phase characteristic boundary value problem for a hyperbolic system and the Kreiss—Lopatinskii condition fails exactly at the poles of the symbols. So the obtained energy estimates exhibit loss of one 
derivative and control of traces of the characteristic part of unknowns. This is a joint work with Ya-Guang Wang (Shanghai Jiaotong University).