Local solvability of real vector fields

Author(s)

Uirá Norberto Matos de Almeida

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2014-02-14

Examining board members

Adalberto Panobianco Bergamasco; Gustavo Hoepfner; José Ruidival Soares dos Santos Filho

• Advisor: Paulo Leandro Dattori da Silva

Abstract

This dissertation aims to study some important results about local solvability of first order differential operators. Specifically, let L be a singular vector field on \'R POT. n\' given by L = \' \\SIGMA SUP. m INF.j=1\' \'a IND. j(x) \'\\PARTIAL SUP. INF. \\PARTIAL x INF. j\'. This work explore the local solvability of L, that is, given f \'IT BELONGS\' \'C POT. INFINITY\' (\'R POT. n\' and \'x INF. 0\' \'IT BELONGS\' \'R POT. n\' we want to find u \'IT BELONGS\' 2 D\'(\'R POT. n) such that Lu = f in a neighborhood of \'x INF. 0\'. We give special attention to the case where the coefficients \'a IND. j\'(x) are linear. We also present some results about local solvability of the equation Lu = cu + f for c \'IT BELONGS\' \'C POT. INFINITY\' (\'R POT. n\') (AU)

• FAPESP's process: 11/14588-4 - Local solvability of real vector fields with linear coeficients
• Grantee: Uirá Norberto Matos de Almeida
• Support Opportunities: Scholarships in Brazil - Master