NONLINEAR DEGENERATE ELLIPTIC-EQUATIONS AND AXIALLY-SYMMETRICAL PROBLEMS

We consider semilinear elliptic equations with a principal part degene rating on a boundary hyperplane. Weak existence, uniqueness and regula rity of solutions are established by variational methods and by reduct ion to uniformly elliptic equations. An important application arises i n the mathematical treatment of the rotating star problem in general r elativity, where the axial symmetry admits the reduction of one of the Einstein equations to a problem of the above farm on a meridian half plane.