On the Gevrey Regularity of Solutions of a Class of Semilinear Elliptic Degenerate Equations on the Plane

Abstract. We investigate the Gevrey regularity (in particular, the analyticity) of solutions of semilinear elliptic degenerate equations on the plane. The method is based on constructing explicit formulas for fundamental solutions and the Friedman effect near boundary. In this paper we deal with the Gevrey regularity (in particular, the ana-lyticity) of solutions of semilinear elliptic degenerate equations of Grushin’s type on R2. We confine with consideration of a model equation, but we belief that the method can be applied to treat more general equations. Recentl