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Solvability for a class of first-order partial differential operators

Grant number: 14/06515-5
Support type:Scholarships abroad - Research
Effective date (Start): October 06, 2014
Effective date (End): July 26, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Paulo Leandro Dattori da Silva
Grantee:Paulo Leandro Dattori da Silva
Host: Adelhamid Meziani
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: Florida International University (FIU), United States  
Associated research grant:12/03168-7 - Geometric theory of PDE and several complex variables, AP.TEM

Abstract

Let X be a two-dimensional, conected, smooth manifold and let L be a nonsingular complex vector field, with smooth coefficients, defined on X. This project deals with the study of problems related to global and semiglobal solvabitity of equations in the form Lu=Au+f defined in X, where A and f are smooth functions. Also, this project deals with the Riemann-Hilbert problem with equationLu=Au+B\overline{u}+f, em U\subset R^2with the boundary condition\Re(gu)=h, on \partial U,where L is a smooth complex vector field defined on R^2, f\in C^\infty(R^2),g\in C^\alpha(\partial U, S^1) andh\in C^\alpha(\partial U, R). (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CAMPANA, C.; DA SILVA, P. L. DATTORI; MEZIANI, A. Riemann-Hilbert problem for a class of hypocomplex vector fields. Complex Variables and Elliptic Equations, v. 62, n. 10, SI, p. 1413-1424, 2017. Web of Science Citations: 1.
DATTORI DA SILVA, P. L.; MEZIANI, A. Cohomology relative to a system of closed forms on the torus. Mathematische Nachrichten, v. 289, n. 17-18, p. 2147-2158, DEC 2016. Web of Science Citations: 1.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.