Let P be a linear partial differential operator with coefficients in the Gevrey class Gs(Tn) where Tn is the n-dimensional torus and sgreater-or-equal, slanted1. We prove that if P is s-globally hypoelliptic in Tn then its transposed operator tP is s-globally solvable in Tn, thus extending to the Gevrey classes the well-known analogous result in the corresponding C∞ class.
Global hypoellipticity and global solvability in Gevrey classes on the n-dimensional torus
Zanghirati L.
2004
Abstract
Let P be a linear partial differential operator with coefficients in the Gevrey class Gs(Tn) where Tn is the n-dimensional torus and sgreater-or-equal, slanted1. We prove that if P is s-globally hypoelliptic in Tn then its transposed operator tP is s-globally solvable in Tn, thus extending to the Gevrey classes the well-known analogous result in the corresponding C∞ class.File in questo prodotto:
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