Qualitative properties for fourth order PDEs arising in differential geometry

• Grant number: 21/15139-0
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: August 01, 2022
• End date: July 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: João Henrique Santos de Andrade
• Supervisor: Juncheng Wei
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of British Columbia, Vancouver (UBC), Canada
• Associated to the scholarship: 20/07566-3 - Qualitative properties for higher order and non-local PDEs arising in Differential Geometry, BP.PD

Abstract

In this project, we address the study of qualitative properties for some geometric fourth order equations. First, we would like to provide general asymptotic expansions for singular solutions to the Q-curvature equation on the punctured ball with a non-flat background metric. Second, we aim to obtain multiplicity and phase transition results for the fourth order Allen-Cahn-Hilliard equation, which as the ultimate goal, by taking the limit when the relaxing parameter goes to zero, would lead to existence results for Willmore boundaries with area 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; 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., 2023-05-23. (20/07566-3, 21/15139-0)