Perturbations of globally hypoelliptic operators
The author investigates when perturbations of globally hypoelliptic (GH) operators on a torus are again GH. It is shown that nonelliptic, constant coefficient, first order operators become generically non-GH whereas operators of order bigger or equal to three possess a stability. In the order-two borderline case examples are discussed where the GH-property is preserved under a parameter dependent perturbation except for a discrete set of a parameters.
globally hypoelliptic operators on a torus
scientific article; zbMATH DE number 703249