A priori estimates for elliptic operators and applications

• Grant number: 18/15484-7
• Support Opportunities: Research Grants - Young Investigators Grants - Phase 2
• Start date: May 01, 2019
• End date: April 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Tiago Henrique Picon
• Grantee: Tiago Henrique Picon
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 13/17636-5 - A priori estimates for elliptic complexes and applications, AP.JP
• Associated research grant(s): 24/14167-9 - Removable singularities for the divergence equation with a linear term, AV.EXT
• Associated scholarship(s): 25/00433-1 - Higher-order elliptic and canceling operators and new advances in Hardy spaces, BE.PQ; 22/02211-8 - Solvability for elliptic and canceling linear differential operators, BP.PD; 22/00874-0 - Boundedness of strongly singular Calderón-Zygmund for Hardy spaces, BP.MS; 21/12655-8 - Characterization of Hardy-Sobolev type spaces and applications, BP.DD; 19/19199-8 - Introduction to the theory of distribution, BP.IC

Abstract

This research inserted into Harmonic Analysis and Linear Partial Differential Equations areas has interest to obtain advances on the following topics: a priori estimates in L1 norm and solvability results to canceling and elliptic differential operators, estimates for elliptic systems of vector fields locally integrable, L1 estimates for elliptic complexes and pseudo-complexes, div-curl type estimates, Hardy spaces and pseudodifferential operators. (AU)

Scientific publications

(9)

(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)

HOEPFNER, G.; KAPP, R.; PICON, T.. On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces. POTENTIAL ANALYSIS, JUL 2020. (19/04995-3, 18/14316-3, 18/15484-7)

MOONENS, LAURENT; PICON, TIAGO. On local continuous solvability of equations associated to elliptic and canceling linear differential operators. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 149, p. 47-72, MAY 2021. (17/17804-6, 18/15484-7, 19/21179-5)

PICON, TIAGO; VASCONCELOS, CLAUDIO. On the Continuity of Strongly Singular Calderon-Zygmund-Type Operators on Hardy Spaces. Integral Equations and Operator Theory, v. 95, n. 2, p. 29-pg., 2023-06-01. (18/15484-7)

HOEPFNER, G.; KAPP, R.; PICON, T.. On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces. POTENTIAL ANALYSIS, v. 55, n. 3, p. 491-512, OCT 2021. (18/14316-3, 19/04995-3, 18/15484-7)

BILIATTO, VICTOR; MOONENS, LAURENT; PICON, TIAGO. Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions. FORUM MATHEMATICUM, v. N/A, p. 6-pg., 2024-10-02. (18/15484-7)

BILIATTO, V.; PICON, T.. Sufficient conditions for local Lebesgue solvability of canceling and elliptic linear differential equations with measure data. Journal of Differential Equations, v. 430, p. 25-pg., 2025-06-15. (18/15484-7)

DAFNI, GALIA; LAU, CHUN HO; PICON, TIAGO; VASCONCELOS, CLAUDIO. Inhomogeneous cancellation conditions and Calderon-Zygmund type operators on h(p). NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 225, p. 22-pg., 2022-08-26. (18/15484-7)

HOUNIE, J.; PICON, T.. Local Hardy-Littlewood-Sobolev inequalities for canceling elliptic differential operators. Journal of Mathematical Analysis and Applications, v. 494, n. 1, p. 24-pg., 2021-02-01. (18/14316-3, 18/15484-7)

DE NAPOLI, PABLO; PICON, TIAGO. STEIN-WEISS INEQUALITY IN L1 NORM FOR VECTOR FIELDS. Proceedings of the American Mathematical Society, v. 151, n. 4, p. 17-pg., 2022-12-01. (18/15484-7)