On the global solvability in Gevrey classes on the n-dimensional torus

Abstract

Let P be a linear partial differential operator with coefficients in the Gevrey class G s ( T n ), where T n is the n-dimensional torus and s⩾1. We prove a necessary condition for the s-global solvability of P on T n . We also apply this result to give a complete characterization for the s-global solvability for a class of formally self-adjoint operators with nonconstant coefficients.