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)

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.