Local solvability and hypoellipticity for semilinear anisotropic partial differential equations

Abstract

We propose a unified approach, based on methods from microlocal analysis, for characterizing the local solvability and hypoellipticity in C ∞ C^\infty and Gevrey G σ G^\sigma classes of 2 2 -variable semilinear anisotropic partial differential operators with multiple characteristics. The conditions imposed on the lower-order terms of the linear part of the operator are optimal.