Global solvability and global hypoellipticity of complex vector fields on surfaces

J Hounie, G Zugliani - Journal of Differential Equations, 2022 - Elsevier
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 …

Solvability near the characteristic set for a class of first‐order linear partial differential operators

WA Cerniauskas… - Mathematische …, 2018 - Wiley Online Library
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 …

C k -solvability near the characteristic set for a class of elliptic vector fields with degeneracies

PL Dattori da Silva, J Marques, ER da Silva - Archiv der Mathematik, 2015 - Springer
This paper deals with the solvability near the characteristic set Σ={0\} * S^ 1 Σ= 0× S 1 of
operators of the form L= ∂/∂ t+(x^ na (x)+ ixb (x)) ∂/∂ x, b (0) ≠ 0\,\rm and\,\, n ≧ 2,\,\rm …

[PDF][PDF] Semiglobal solvability for a class of first order operators

WA Cerniauskas, PL Dattori da Silva… - Matemática …, 2022 - repositorio.usp.br
In this work, we deal with solvability near the characteristic set of equations in the form Lu=
pu+ f, where the operator L=∂ t+(xna (x)+ ixb (x))∂ x is defined on Ω= R× S1, a and b are …

Resolubilidade perto do conjunto característico para uma classe de campos vetoriais complexos

LS Hernandez - 2016 - teses.usp.br
Esta dissertação expõe sobre a resolubilidade do campo vetorial complexo L= â/â t+(a (x)+
ib (x)) â/â x, b ⢠0 definido em Ω ε=(-ε, ε) à S1, ε> 0, perto do conjunto característico …