Approximate solutions of vector fields and an application to Denjoy–Carleman regularity of solutions of a nonlinear PDE

Abstract

In this paper we study microlocal regularity of a  2 -solution of the equation) is ultradifferentiable in the variables ( , ) ∈ ℝ × ℝ and holomorphic in the variables () ∈ ℂ × ℂ . We proved that if   is a regular Denjoy-Carleman class (including the quasianalytic case) then:where WF  ( ) is the Denjoy-Carleman wave-front set of and Char( ) is the characteristic set of the linearized operator :