Hypoellipticity of Nonlinear Partial Differential Equations

In this paper, we study the hypoellipticity problems for fully nonlinear panial differential equations of order m. For a solution u ∈ C^p_{loc}(Ω), if the linearized operator for the nonlinear equation on u satisfies some subelliptic conditions, we can deduce u ∈ C^∞(Ω) by using the paradifferential operator theory of J. -M. Bony.