Advanced search
Start date

Solvability and hypoellipticity of first order partial differential operators and boundary value problems


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)

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

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)
DATTORI DA SILVA, PAULO L.; ZAPATA, MIGUEL A. C. Gevrey semiglobal solvability for a class of complex vector fields. Complex Variables and Elliptic Equations, APR 2021. Web of Science Citations: 0.
DA SILVA, P. L. DATTORI; MEZIANI, A. A Gevrey Differential Complex on the Torus. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 26, n. 1 JAN 14 2020. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: