| Grant number: | 18/15046-0 |
| Support Opportunities: | Regular Research Grants |
| Start date: | November 01, 2018 |
| End date: | April 30, 2021 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Paulo Leandro Dattori da Silva |
| Grantee: | Paulo Leandro Dattori da Silva |
| Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
| City of the host institution: | São Carlos |
Abstract
Let X be smooth, connected, n-dimentional manifold and let \mathcal{L} be a nonsingular smooth complex vector field defined on X.This project deals with the study of problems related with semiglobal/global solvability and global hypoellipticity of equations in the form\mathcal{L}u=Au+B\overline{u}+fdefined in X, where A, B and f are smooth functions.Also, it deals with the study of generalized Riemann-Hilbert problem\left\{\begin{array}{lll}Lu=Au+B\overline{u}+f,& \textrm{em} & \mathcal{U}\subset\mathbb{R}^2\\\Re(gu)=\chi, \quad & \textrm{sobre} & \partial\mathcal{U}\end{array}\right.,where L is a smooth complex vector field defined on R^2, f\in C^\infty(R^2), g\in C^\alpha(\partial\mathcal{U}, S^1) and \chi\in C^\alpha(\partial\mathcal{U}, R).The problems mentioned above can be considered in others spaces of functions, for instance, L^p.This project also deals with the study of solvability and hipoellipticity of complex associated to a system of closed 1-formsdefined on compact manifolds. (AU)
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