Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2016.tde-09112016-161310
Document
Author
Full name
Lorena Soriano Hernandez
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Silva, Paulo Leandro Dattori da (President)
Ebert, Marcelo Rempel
Silva, Maurício Fronza da
Zani, Sergio Luis
Title in Portuguese
Resolubilidade perto do conjunto característico para uma classe de campos vetoriais complexos
Keywords in Portuguese
Campo vetorial complexo
Conjunto característico
Resolubilidade
Abstract in Portuguese
Esta dissertação expõe sobre a resolubilidade do campo vetorial complexo L = ∂ /∂t +(a(x) + ib(x))∂/∂x, b ≢ 0 definido em Ωε = (-ε, ε) × S1, ε > 0, perto do conjunto característico Σ = {0} × S1, sendo a e b funções de classe C∞ em (- ε, ε) a valores reais. Os resultados apresentados mostram que a resolubilidade de L em uma vizinhança cheia de Σ depende da relação entre as ordens de anulamento de a e b em x = 0.
Title in English
Solvability near the characteristic set for a class of complex vector fields
Keywords in English
Characteristic set
Complex vector field
Solvability
Abstract in English
This dissertation deals with the solvability of complex vector fieldL = ∂ /∂t +(a(x) + ib(x))∂/∂x, b ≢ 0 defined on Ωε = (-ε ε) × S1, ε > 0, near the characteristic set Σ = {0} × S1, where a and b are C∞ real-valued functions in (- ε, ε). The presented results show hat solvability of L in a full neighborhood of Σ depends on the interplay between the order of vanishing of the functions and a and b at x = 0.
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Publishing Date
2016-11-10