Qualitative properties for geometric differential equations

• Grant number: 23/15567-8
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2024
• End date: January 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: João Henrique Santos de Andrade
• Grantee: João Henrique Santos de Andrade
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated researchers: Guillermo Sebastian Henry ; Jesse Ratzkin ; JOAO MARCOS BEZERRA DO Ó ; Juncheng Wei

Abstract

This project aims to study qualitative properties for some geometric differential equations arising in differential geometry and geometric measure theory. First, we would like to provide general qualitative properties for singular solutions to the Q-curvature equation on punctured domains. Second, we aim to obtain multiplicity and phase transition results for the Allen-Cahn-Hilliard equation, which, by taking the limit when the relaxing parameter goes to zero, would lead to existing results for perimeter-minimizers boundaries under some geometrical constraints. (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)

ANDRADE, JOAO HENRIQUE; WEI, JUNCHENG. Asymptotics for positive singular solutions to subcritical sixth order equations. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 255, p. 28-pg., 2025-06-01. (23/15567-8, 21/15139-0, 20/07566-3)