Differential operators of infinite order in the study of regularity and solvability of linear and nonlinear PDE's

• Grant number: 16/13620-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2016
• End date: October 23, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gustavo Hoepfner
• Grantee: Luis Fernando Ragognette
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM
• Associated scholarship(s): 17/13450-5 - On the reflection principle for hypo-analytic structures, BE.EP.PD

Abstract

This project is in great part the natural extension of the work realized in the Ph.D. Thesis of the candidate, which in turn is the extension of the Caetano’s Ph.D. Thesis, [10], and of the papers of Cordaro, [13], and Caetano and Cordaro, [11]. Both the candidate and the supervisor believe that the techniques involved in the study of infinite order operators can be applied in other contexts. In a summarized manner, we want to explore these ideas to obtain representation's theorems for other classes of ultradifferentiable functions or to prove representation theorems under weaker the conditions for the operators. We are also interested in to find relations between infinite order operators and the boundary value of holomorphic functions and, if succeed, we are going to investigate the possible applications in microlocal analysis. Finally, the goal of the last problem proposed here is to extend to context of hyperfunctions a result of Hanges and Treves, [15] about the regularity of the solutions of a non-linear operator. (AU)

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)

ARAUJO, GABRIEL; FERRA, IGOR A.; RAGOGNETTE, LUIS F.. GLOBAL ANALYTIC HYPOELLIPTICITY AND SOLVABILITY OF CERTAIN OPERATORS SUBJECT TO GROUP ACTIONS. Proceedings of the American Mathematical Society, v. 150, n. 11, p. 13-pg., 2022-07-29. (16/13620-5)

HOEPFNER, GUSTAVO; MEDRADO, RENAN D.; RAGOGNETTE, LUIS F.. The Baouendi-Treves approximation theorem for Gevrey classes and applications. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, v. 23, n. 1, p. 24-pg., 2022-01-01. (17/13450-5, 17/03825-1, 19/04995-3, 16/13620-5)

ARAUJO, GABRIEL; FERRA, IGOR A.; RAGOGNETTE, LUIS F.. Global solvability and propagation of regularity of sums of squares on compact manifolds. JOURNAL D ANALYSE MATHEMATIQUE, v. 148, n. 1, p. 34-pg., 2022-08-25. (18/12273-5, 16/13620-5)