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# A Note about Analytic Solvability of Complex Planar Vector Fields with Degeneracies

Published:2011-02-10
Printed: Jun 2011
• Paulo L. Dattori da Silva,
Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Departamentoėwline de Matemática, Caixa Postal 668, São Carlos - SP, 13560-970 Brazil
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## Abstract

This paper deals with the analytic solvability of a special class of complex vector fields defined on the real plane, where they are tangent to a closed real curve, while off the real curve, they are elliptic.
 Keywords: semi-global solvability, analytic solvability, normalization, complex vector fields, condition~($\mathcal P$)
 MSC Classifications: 35A01 - Existence problems: global existence, local existence, non-existence 58Jxx - Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]

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