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Local solvability of real vector fields

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Uirá Norberto Matos de Almeida
Total Authors: 1
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:
Examining board members:
Adalberto Panobianco Bergamasco; Gustavo Hoepfner; José Ruidival Soares dos Santos Filho
Advisor: Paulo Leandro Dattori da Silva

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 type: Scholarships in Brazil - Master