Advanced search
Start date

Local solvability of rotationally invariant differential forms

Grant number: 20/14106-9
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): April 01, 2021
Effective date (End): February 28, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Paulo Leandro Dattori da Silva
Grantee:Fernanda Martins Simão
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM


We will deal with local solvability of classes of linear partial differential operators. More precisely, we will deal with solvability of classes of first order differential equations in context of differential forms. Let \Omega=A(z)dz+B(z)d\bar{z} be a smooth differential 1-form defined in a neighborhood of the origin in \mathbb{R}^2. We say that \Omega is rotationally invariant if \Omega\wedge R^*_\alpha\Omega=0 for all rotation of angle \alpha, R_\alpha, of \mathbb{R}^2. Let \Omega be a rotationally invariant smooth differential 1-form, singular at (0,0) and elliptic for all (x,y)\in\mathbb{R}^2\setminus{(0,0)}. We are interested in studying equations in the formdu\wedge\Omega=\eta\wedge\Omega,where \eta is a smooth differential 1-form defined in a neighborhood of the origin of \mathbb{R}^2. The relation between the order of the vanishing of the 2-forms\Omega\wedge\overline{\Omega} and \Omega\wedge(\bar{z}dz+zd\bar{z}) has influence in the solvability. (AU)

News published in Agência FAPESP Newsletter about the scholarship:
Articles published in other media outlets (0 total):
More itemsLess items

Please report errors in scientific publications list by writing to: