Analytic Estimates for Solutions of the Levi Equations

In this paper we introduce a new technique of real analysis for studying the regularity properties of a solution u to the Levi equation in R3. First we study the solution in suitable Sobolev spaces and establish some a priori estimates of analytic type for the “intrinsic” derivatives of the solution. Then we prove that for every ξ0 in the domain there exists a real analytic 2-dimensional manifold Mξ0 passing through ξ0 such that u Mξ0 is an harmonic function.