Global solvability and global hypoellipticity in Gevrey classes for vector fields on the torus

Author(s)

Bergamasco, A. P. ^[1] ; Dattori da Silva, P. L. ^[1] ; Gonzalez, R. B. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Fed Parana, Dept Matemat, Caixa Postal 19081, BR-81531990 Curitiba, Parana - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 264, n. 5, p. 3500-3526, MAR 1 2018.
• Web of Science Citations: 1

Abstract

Let L = partial derivative/partial derivative t + Sigma(N)(j=1) (a(j)+ib(j)) (t) partial derivative/partial derivative x(j) be a vector field defined on the torus TN+1 similar or equal to RN+1 /2 Pi Z(N+1,) where a(j),b(j) are real-valued functions and belonging to the Gevrey class G(s)(T-1), s > 1, for j= 1,..., N. We present a complete characterization for the s-global solvability and s-global hypoellipticity of L. Our results are linked to Diophantine properties of the coefficients and, also, connectedness of certain sublevel sets. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
• Grantee: Jorge Guillermo Hounie
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/20815-4 - Solvability and hypoellipticity of first order partial differential operators and the Riemann-Hilbert problem
• Grantee: Paulo Leandro Dattori da Silva
• Support Opportunities: Regular Research Grants