Problems of maximum and minimum: Isoperimetric inequality and applications

• Grant number: 23/04927-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2023
• End date: June 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Olimpio Hiroshi Miyagaki
• Grantee: Livia Ribeiro Marques Camilo
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

For the duration of this project, the intention is the study of a few of the maximum and minimum problems, enfasizing the study of Isoperimetric Inequality and its many applications.Said knowledge will be given as the infrastructure needed to the study of the Fourier series, once this is one of the most specific objects of study. Henceforth, it also will be studied an introduction to Sobolev spaces and optimization problems (more especifically, minimums) with the intention of globalizing the knowledge of the scholarship student, not only in the area of Mathematics, but also in general habilities for research and building of understanding.