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Qualitative properties for higher order and non-local PDEs arising in Differential Geometry

Grant number: 20/07566-3
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date: February 01, 2021
End date: October 19, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Paolo Piccione
Grantee:João Henrique Santos de Andrade
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis, AP.TEM
Associated scholarship(s):21/15139-0 - Qualitative properties for fourth order PDEs arising in differential geometry, BE.EP.PD

Abstract

In this project, we are concerned with some qualitative properties for solutions to higher order and nonlocal partial differential equations arising in differential geometry. More precisely, we are interested in local asymptotic behavior and multiplicity results for generalizations of the Yamabe and Allen-Cahn equations. (AU)

News published in Agência FAPESP Newsletter about the scholarship:
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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)
ANDRADE, JOAO HENRIQUE; DO O, JOAO MARCOS. QUALITATIVE PROPERTIES FOR SOLUTIONS TO CONFORMALLY INVARIANT FOURTH ORDER CRITICAL SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. N/A, p. 35-pg., . (20/07566-3, 21/15139-0)
ANDRADE, JOAO HENRIQUE; DO O, JOAO MARCOS; RATZKIN, JESSE. Compactness Within the Space of Complete, Constant Q-Curvature Metrics on the Sphere with Isolated Singularities. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v. N/A, p. 21-pg., . (20/07566-3)
ANDRADE, JOAO HENRIQUE; DO O, JOAO MARCOS. Qualitative properties for solutions to subcritical fourth order systems*. Nonlinearity, v. 35, n. 10, p. 48-pg., . (20/07566-3)