A priori estimates for solutions of certain elliptic quasi-linear PDEs, with applications to Geometric Analysis

• Grant number: 25/01840-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: June 01, 2025
• End date: November 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Paolo Piccione
• Visiting researcher: Jaime Bruck Ripoll
• Visiting researcher institution: Instituto De Matemática/Im/Ufrgs, Brazil
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 22/16097-2 - Modern methods in differential geometry and geometric analysis, AP.TEM

Abstract

The technique of a priori estimates for solutions of elliptic PDEs is one of the most powerful and widely used tools in the analysis of this class of equations. It enables addressing problems such as the existence and uniqueness of solutions, the equicontinuity of families of solutions in non-compact domains with respect to certain norms, as well as the construction of specific barriers for special domains.In this project, these techniques will be applied to the study of three main problems described in the research plan. (AU)