Nonlinear Partial Differential Equations: Well-Posedness and Regularity Theory

• Grant number: 15/13011-6
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2015
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Edgard Almeida Pimentel
• Grantee: Edgard Almeida Pimentel
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

This project focuses on the Analysis of Partial Differential Equations (PDEs, for short) and proposes the study of the existence and regularity of solutions to a few problems in the aforementioned field. It relies upon two main subjects: the regularity theory for fully nonlinear elliptic equations and the well-posedness of mean-field games systems, in appropriate classes of solutions. By examining certain model-problems, we seek to further the development of this theory and extend its scope to a broader class of topics in the realm of Analysis of PDEs. (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)

PIMENTEL, EDGARD A.; TEIXEIRA, EDUARDO V.. Sharp Hessian integrability estimates for nonlinear elliptic equations: An asymptotic approach. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 106, n. 4, p. 744-767, OCT 2016. (14/15795-1, 15/13011-6)

PIMENTEL, EDGARD A.; VOSKANYAN, VARDAN. Regularity for Second-Order Stationary Mean-Field Games. Indiana University Mathematics Journal, v. 66, n. 1, p. 1-22, 2017. (15/13011-6)

CIRANT, MARCO; GOMES, DIOGO A.; PIMENTEL, EDGARD A.; SANCHEZ-MORGADO, HECTOR. ON SOME SINGULAR MEAN-FIELD GAMES. JOURNAL OF DYNAMICS AND GAMES, v. 8, n. 4, p. 21-pg., 2020-05-20. (15/13011-6)

GOMES, DIOGO A.; PIMENTEL, EDGARD. TIME-DEPENDENT MEAN-FIELD GAMES WITH LOGARITHMIC NONLINEARITIES. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 47, n. 5, p. 3798-3812, 2015. (15/13011-6)

CASTILLO, RICARDO; PIMENTEL, EDGARD A.. Interior Sobolev regularity for fully nonlinear parabolic equations. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 56, n. 5, OCT 2017. (15/13011-6)