Abstract
A fundamental result in the theory of elliptic PDEs shows that the hessian of solutions of uniformly elliptic PDEs belong to the Sobolev space ��^2,ε. New results show that for the right choice of c, the optimal hessain integrability exponent ε* is given by
ε* = ������ ����(1−������) / ����(1−��), �� ∈ (0,1)
Through the techniques of asymptotic analysis, the behavior and properties of this function are better understood to establish improved quantitative estimates for the optimal integrability exponent in the ��^2,ε-regularity theory.
Thesis Completion
2023
Semester
Spring
Thesis Chair/Advisor
Teixeira, Eduardo
Degree
Bachelor of Science (B.S.)
College
College of Sciences
Department
Mathematics
Language
English
Access Status
Open Access
Release Date
5-15-2023
Recommended Citation
Hernandez, David, "Asymptotic Regularity Estimates for Diffusion Processes" (2023). Honors Undergraduate Theses. 1358.
https://stars.library.ucf.edu/honorstheses/1358