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Semiglobal solvability for classes of non singular vector fields

Grant number: 17/20664-1
Support type:Scholarships in Brazil - Master
Effective date (Start): March 01, 2018
Effective date (End): February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Paulo Leandro Dattori da Silva
Grantee:Vinícius Novelli da Silva
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Let V be a connected N-dimensional smooth manifold and let L be a non singular smooth complex vector field defined on V. Local solvability is characterized by Nirenberg-Treves condition (P).The solvability of L is still an open problem if we consider the semiglobal problem. Let K be a compact set of V. We say that L is solvable at K if for any f belonging to afinite codimension subspace of C^\infty(V) there is a distribution u solution to the equation Lu=f in a neighborhood of K. Condition (P) is also necessary to semiglobal solvability. It is sufficient provided that a certain geometric condition (GC), due to Hormander, is satisfied. This work deals with the solvability for classes of vector fields that do not satisfy (GC). More precisely, solvability at \mathbb{T}^m\times\{0\}, where \mathbb{T}^m is the torus \mathbb{T}^m\simeq\mathbb{R}^m/2\pi\mathbb{Z}^m, for classes of vector fields defined on\mathbb{T}^m\times\mathbb{R}^n, in the case where \mathbb{T}^m\times\{0\} contains orbits (in the sense of Sussmann) of L. (AU)

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
SILVA, Vinícius Novelli da. Semiglobal solvability for classes of non-singular vector fields. 2020. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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