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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Classes of globally solvable involutive systems

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Author(s):
Bergamasco, Adalberto [1] ; Parmeggiani, Alberto [2] ; Zani, Sergio [1] ; Zugliani, Giuliano [3, 1]
Total Authors: 4
Affiliation:
[1] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna - Italy
[3] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS; v. 8, n. 4, p. 551-583, DEC 2017.
Web of Science Citations: 4
Abstract

We study a linear operator associated with a real smooth closed non-exact 1-form b defined on a closed orientable surface. Locally the operator can be seen as an overdetermined system of first order linear partial differential equations. Here we present a result that completely characterizes a class of systems that are globally solvable, namely when b has rank equal to 1, in terms of a topological condition. Such a condition bears on the superlevel and sublevel sets of primitives of b. In a certain covering space, called minimal covering space, the condition is equivalent to the connectedness of the superlevel and sublevel sets of the primitives there defined (a property that frequently appears in related papers). We furthermore exhibit another class of globally solvable systems by constructing smooth closed non-exact 1-forms of arbitrary rank on surfaces of genus greater than 1 out of 1-forms which individually define globally solvable systems on tori. (AU)

FAPESP's process: 12/05355-9 - Global properties of involutive systems on compact manifolds
Grantee:Giuliano Angelo Zugliani
Support type: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
Grantee:Jorge Guillermo Hounie
Support type: Research Projects - Thematic Grants