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

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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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.; DATTORI DA SILVA, P. L. Solvability in the Large and Boundary Value Problems for Mizohata Type Operators. Results in Mathematics, v. 77, n. 2 APR 2022. Web of Science Citations: 0.
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.

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