In this work we consider systems of two smooth vector fields on the three-dimensional torus
associated to a closed 1-form. We prove that, for such systems, the global solvability in the …

We study the finiteness of range's codimension for a class of non-globally hypoelliptic vector
fields on a torus of dimension three. The linear dependence of certain interactions of the …

The goal of this paper is study the global solvability of a class of complex vector fields of the
special form L=∂/∂ t+ (a+ ib)(x)∂/∂ x, a, b∈ C∞(S1; R), defined on two-torus T2≅ …

We consider a class of systems of two smooth vector fields on the 3-torus associated to a
closed 1-form. We prove that the global solvability is completely determined by the …

We study a class of complex vector fields defined on the two-torus of the form L=∂/∂ t+ (a
(x, t)+ ib (x, t))∂/∂ x, a, b∈ C∞(T2; R), b≢ 0. We view L as an operator acting on smooth …

This paper deals with semi-global C k-solvability of complex vector fields of the form L= ∂/∂
t+ x^ r (a (x)+ ib (x)) ∂/∂ x,, r≥ 1, defined on\Omega_ ϵ=(-ϵ, ϵ) * S^ 1, ϵ> 0, where a and b …

We consider smooth, nonvanishing complex (not essentially real) vector fields L= X+ i Y that
satisfy the Nirenberg-Treves condition (P) and are allowed to possess some closed one …

We study the Gevrey solvability of a class of complex vector fields, defined on Ωϵ=(− ϵ, ϵ)×
S1, given by L=∂/∂ t+ (a (x)+ ib (x))∂/∂ x, b≢ 0, near the characteristic set Σ={0}× S1. We …

In this work we deal with solvability of first‐order differential equations in the form, where L is
a planar complex vector field, elliptic everywhere except along a simple closed curve Σ on …

This work deals with the solvability near the characteristic set Σ= 0× S 1 of operators of the
form L= ∂/∂ t+(x^ na (x)+ ix^ mb (x)) ∂/∂ x, b\not\equiv0 and a (0)≠ 0, defined on\Omega …