Keywords
Regularity Theory, Elliptic PDES
Abstract
The study of the calculus of variations is largely motivated by physical phenomena which can often be seen through the lens of minimizing a system’s energy. In this paper, we will survey the 19th Hilbert problem and the revolutionary approach by Ennio De Giorgi to solve it. The 19th Hilbert problem asks whether minimizers of regular variational problems are necessarily analytic. In simple terms, if we have a function that minimizes a nicely behaved functional, are the minimizers themselves nicely behaved? The methods established by De Giorgi have greatly influenced the current study of nonlinear elliptic partial differential equations.
Thesis Completion Year
2025
Thesis Completion Semester
Spring
Thesis Chair
Teixeira, Eduardo
College
College of Sciences
Department
Department of Mathematics
Thesis Discipline
Mathematics
Language
English
Access Status
Campus Access
Length of Campus Access
5 years
Campus Location
Orlando (Main) Campus
STARS Citation
Santori, Luis E., "19th Hilbert Problem: Regularity Of Minimizers" (2025). Honors Undergraduate Theses. 312.
https://stars.library.ucf.edu/hut2024/312