Dissertation
Regularity of a degenerate equation
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Autumn 2020
DOI: 10.17077/etd.005663
Abstract
The Laplacian operator is an isomorphism from s regular functions to s-2 regular functions, for s that is not an integer with inequality controls. When s is an integer it is critical, and the controls need to be modified. This result was extended to the operators L that is degenerate by Lihe Wang (2003). However, the boundary regularity was left undone, and the critical cases are still open. These problems are solved in this thesis by considering the intrinsic distance Holder spaces. Furthermore, the degenerate diffusion equation with nonlocal terms are considered, and Holder regularity is derived.
Details
- Title: Subtitle
- Regularity of a degenerate equation
- Creators
- Tao Wang
- Contributors
- Lihe Wang (Advisor)Tong Li (Committee Member)Xiaoyi Zhang (Committee Member)Palle Jorgensen (Committee Member)Wei Li (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Mathematics
- Date degree season
- Autumn 2020
- DOI
- 10.17077/etd.005663
- Publisher
- University of Iowa
- Number of pages
- v, 158 pages
- Copyright
- Copyright 2020 Tao Wang
- Language
- English
- Description bibliographic
- Includes bibliographical references (pages 150-158).
- Public Abstract (ETD)
The thesis considers an equation genesis from fluid dynamics and mathematical finance. Precise Hӧlder estimates are proved for the solutions and their derivatives. The Hӧlder continuity of the solutions is also proved from the stochastic approach.
- Academic Unit
- Mathematics
- Record Identifier
- 9984036086502771
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