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

• 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

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)

Scientific publications

(6)

(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)

DE ALMEIDA, MARCELO F.; DATTORI DA SILVA, PAULO L.. Solvability of a Class of First Order Differential Operators on the Torus. Results in Mathematics, v. 76, n. 2, p. 17-pg., 2021-05-01. (18/14316-3, 18/15046-0)

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. (16/21969-8, 18/14316-3, 18/15046-0)

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. (18/14316-3, 18/15046-0)

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. (18/14316-3, 18/15046-0)

DATTORI DA SILVA, PAULO L.; ZAPATA, MIGUEL A. C.. Gevrey semiglobal solvability for a class of complex vector fields. Complex Variables and Elliptic Equations, v. 67, n. 9, p. 11-pg., 2021-04-14. (18/14316-3, 18/15046-0)

ARAUJO, GABRIEL; BERGAMASCO, ADALBERTO P.; DA SILVA, PAULO DATTORI L.. Gevrey semiglobal solvability for a class of elliptic vector fields with degeneracies. Mathematische Nachrichten, v. N/A, p. 20-pg., 2023-05-20. (18/14316-3, 18/15046-0, 18/12273-5)