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Dissertation
A study of p-variation and the p-Laplacian for 0 < p ≤ 1 and finite hyperplane traversal algorithms for signal processing
Washington State University
Doctor of Philosophy (PhD), Washington State University
2013
DOI:
https://doi.org/10.7273/000005543
Abstract
In this work (freely available by contacting the author), we study and find minimizers of the problem min ZΩ |∇u|p + λ|f − u|dx, for 0 < p ≤ 1,
where Ω ⊂ Rn is an open bounded convex set. We find fast algorithms that find minimizers for the p = 1 problem and local minimizers for the p < 1 problem. Our algorithms solve the minimization problem for p = 1 for all λ at the computational cost of solving only the λ = 0 problem. We also find and characterize the set of minimizers of the λ = 0 problem. We compare minimizers to stationary solutions to the p-Laplacian evolution equation ut = ∆pu, for 0 < p < 1. We also consider a curvature approach to understanding the nature of the evolution in this equation. We use the curvature understanding to find families of classical stationary solutions.
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Details
- Title
- A study of p-variation and the p-Laplacian for 0 < p ≤ 1 and finite hyperplane traversal algorithms for signal processing
- Creators
- Heather A. Van Dyke
- Contributors
- Thomas J Asaki (Advisor)Kevin R Vixie (Committee Member)David J Wollkind (Committee Member)Matthew B Rudd (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 188
- Identifiers
- 99901052238301842
- Language
- English
- Resource Type
- Dissertation