On the Solvability of a Class of Second Order Degenerate Operators

Solvability of Subprincipal Type Operators

“…One limit is when ξ → 0 for fixed Λ and then the limit of (1. 19) is equal to ∂ t +Re C •∂ x which gives the subprincipal bicharacteristics. We can also take τ = Λτ 0 , η = Λη 0 and…”

“…This paper treats subprincipal type operators with involutive characteristics having nondegenerate second order vanishing of the principal symbol. For the noninvolutive or degenerate cases, see [19], [20] and the references there.…”

Carleman estimates for third order operators of KdV and non KdV-type and applications

“…In this paper, we will continue the investigation of some variable coefficient PDOs (partial differential operators) built from a system of real smooth vector fields, initiated in the works [13,15,18,19] (see also [12,14,17]). Since when the celebrated works by Kolmogorov [31] first, and by Hörmander [24] afterwards, about the hypoellipticity of operators written as sums of squares of vector fields were published, a lot of connected problems have been investigated.…”

“…The use of the vanishing function is twofold: on one side it adds degeneracy to a model which is already degenerate by itself, on the other side it permits to include in the treatment some operators generalizing the Kannai operator, that is operators having a changing sign principal symbol. The introduction of the vanishing function requires a price to pay, price which is given in terms of conditions on the lower order terms of the operators (see [12,14,17] for an overview of such results). Nevertheless, the classes studied in these works encompass different lower order terms, which makes it possible to include parabolic-type operators, Schrödinger-type operators, a blend of the two, and some prototypes with non-smooth coefficients.…”