﻿ Research Grants 18/15046-0 - Equações diferenciais parciais, Resolubilidade global - BV FAPESP
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Solvability and hypoellipticity of first order partial differential operators and boundary value problems

 Grant number: 18/15046-0 Support type: Regular Research Grants Duration: November 01, 2018 - April 30, 2021 Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis Principal researcher: Paulo Leandro Dattori da Silva Grantee: Paulo Leandro Dattori da Silva Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

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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