Lokale Auflösbarkeit von Differentialoperatoren erster Ordnung in einem kritischen Punkt. (Local solvability of first order differential operators in a critical point)
Let \(D=\sum ^{n}_{i=1}h_ i \partial /\partial x_ i+b\) be a first order differential operator with a critical point p (i.e. \(h_ i(p)=0\) for \(i=1,...,n)\). We give sufficient conditions for D to be locally solvable at the point p (Theorem 3.1). Our method is to transform D into an operator \~D with linear coefficients using Sternberg's linearization theorem and to prove a global solvability result for \~D (Corollary 2.2).
scientific article; zbMATH DE number 3973395