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

• Grant number: 20/07566-3
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): February 01, 2021
• Effective date (End): January 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Paolo Piccione
• Grantee: João Henrique Santos de Andrade
• Home 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

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)