Semiglobal solvability for classes of non singular vector fields

• Grant number: 17/20664-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Leandro Dattori da Silva
• Grantee: Vinícius Novelli da Silva
• Host 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)

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.