Periodic variational problem related with linear Reynolds equation

Periodical problem on microgeometry optimization of bearing on gas oiling by criterion of lifting force maximum is considered. Pressure field in gas layer is determined by Reynolds equation of gas oiling. The case of compressibility small numbers is studied. The analysis is carried out of the system of conditions necessary for variational problem extremum on the basis of which the existence of optimal profile with infinite number of ruptures was determined. Threshold periodical optimal profiles are found.