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.
Bachelor of Science (B.S.)
College of Sciences
Hernandez, David, "Asymptotic Regularity Estimates for Diffusion Processes" (2023). Honors Undergraduate Theses. 1358.