Vector fields, sums of squares and Bers-Vekua equations: existence and regularity of solutions

• Grant number: 21/03199-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2021
• End date: February 15, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Adalberto Panobianco Bergamasco
• Grantee: Bruno de Lessa Victor
• 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

Abstract

This project mainly consists of two research areas we intend to deal with: the first one relates to global analysis on the torus in the ultradifferentiable setting; we are particularly interested in global solvability and hypoellipticity (in the Denjoy-Carleman frame) for complex vector fields and operators given by sums of squares of vector fields. The second part is concerned with infinitesimal bendings of two-dimensional surfaces with nonnegative Gaussian curvature and its connection with solvability of Bers-Vekua equations for planar complex vector fields with singularities. (AU)

Scientific publications

(5)

(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)

ARAUJO, G.; DA SILVA, P. L. DATTORI; VICTOR, B. DE LESSA. Global Analytic Solvability of Involutive Systems on Compact Manifolds. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 5, p. 30-pg., 2023-05-01. (18/14316-3, 18/12273-5, 21/03199-9)

VICTOR, B. DE LESSA; MEZIANI, ABDELHAMID. Infinitesimal bendings for classes of two-dimensional surfaces. Complex Variables and Elliptic Equations, v. N/A, p. 23-pg., 2022-09-08. (21/03199-9)

VICTOR, B. DE LESSA; MEZIANI, ABDELHAMID. A generalized CR equation with isolated singularities. Complex Variables and Elliptic Equations, v. N/A, p. 13-pg., 2022-06-02. (21/03199-9)

ARAUJO, G.; DATTORI DA SILVA, P. L.; VICTOR, B. DE LESSA. Global analytic hypoellipticity of involutive systems on compact manifolds. MATHEMATISCHE ANNALEN, v. N/A, p. 26-pg., 2022-07-18. (18/14316-3, 21/03199-9, 18/12273-5)

ARIAS JUNIOR, ALEXANDRE; VICTOR, BRUNO DE LESSA. The Cauchy problem for a class of linear degenerate evolution equations on the torus. Journal of Mathematical Analysis and Applications, v. 542, n. 1, p. 38-pg., 2024-08-16. (21/03199-9, 22/01712-3)