Propagation of singularities for operators with contant coefficient hyperbolic-elliptic principal part
The authors consider partial differential operators of the type \(P(x,D)=P_ m(D)+Q(x,D),\) where the principal part \(P_ m\) is independent of x and is assumed to be hyperbolic-elliptic. They study the propagation of Gevrey singularities for the solutions u of the equation \(P(x,D)u=f\), for ultradistributions f, and find exactly to which spaces of ultradistributions u microlocally belongs. The results are obtained by constructing a fundamental solution for P when the lower order part is with constant coefficients, and otherwise by contructing a left parametrix to analyze the propagation of singularities. By using a right parametrix, the result on the semiglobal solvabiliy of (1), modulo analytic functions, is obtained.
scientific article; zbMATH DE number 4065562
scientific article