Hypoellipticity of systems of pseudo differential operators with double characteristics
The author considers the hypoellipticity of a system of pseudo- differential operators on \(\Omega\), an open subset of \({\mathbb{R}}^ N\), of the form \[ P(x,D)=I_ dp(x,D)+Q(x,D), \] where \(I_ d\) is the identity \(d\times d\) matrix, p(x,D) a scalar pseudodifferential operator of degree m, and Q(x,D) a \(d\times d\) system of pseudodifferential operator of degree at most m-1. He obtains sufficient conditions for p(x,D) to be hypoelliptic, which extend the results of the author [Commun. Partial Differ. Equations 10, 525-542 (1985; Zbl 0577.35025)] to the vector situation with no restriction on codimension of \(\Sigma\).
scientific article; zbMATH DE number 4150801