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.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:honorstheses-2543 |
| Date | 01 January 2023 |
| Creators | Hernandez, David |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Honors Undergraduate Theses |
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