Finite Difference Methods for the p-Laplacian

Mapel, Jesse Austin (2018) Finite Difference Methods for the p-Laplacian. Masters thesis, Northern Arizona University.

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Abstract

The p-Laplacian is a non-linear, differential operator whose eigenvalues and eigenfunctions have been studied for many decades. On domains in $\mathbb{R}$, they are well known and can be easily computed. For domains in $\mathbb{R}^2$, its spectra has been partially characterized but it is unkown if this characterization is exhaustive. Because of its challenging numerical properties, many different methods have been proposed for computing its eigenvalues and eigenvectors. We propose a new approach based on two step finite difference methods that compliments existing approaches and may be able to find eigenvalues and eigenvectors that previous approaches could not.

Item Type:	Thesis (Masters)
Publisher’s Statement:	© Copyright is held by the author. Digital access to this material is made possible by the Cline Library, Northern Arizona University. Further transmission, reproduction or presentation of protected items is prohibited except with permission of the author.
Keywords:	Finite Differences; Newton's Method; p-Laplacian
Subjects:	Q Science > QA Mathematics
NAU Depositing Author Academic Status:	Student
Department/Unit:	College of the Environment, Forestry, and Natural Sciences > Mathematics and Statistics
Date Deposited:	26 Apr 2021 19:43
URI:	http://openknowledge.nau.edu/id/eprint/5285

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