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

Subjects

Calculus of variations; Variational principles; Nonlinear functional analysis; Geometric analysis; Mathematical physics--Research

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Restricted to the UCF community until 5-15-2030; it will then be open access.

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Rights Statement

In Copyright