Approximation of the second eigenvalue of the $p$-Laplace operator in symmetric domains
Spectral Theory
2020-02-24 v2
Abstract
A new idea to approximate the second eigenfunction and the second eigenvalue of -Laplace operator is given. In the case of the Dirichlet boundary condition, the scheme has the restriction that the positive and the negative part of the second eigenfunction have equal -norm, however, in the case of Neumann boundary condition, our algorithm has not such restriction. Our algorithm generates a descending sequence of positive numbers that converges to the second eigenvalue. We give various examples and computational tests.
Keywords
Cite
@article{arxiv.1907.13390,
title = {Approximation of the second eigenvalue of the $p$-Laplace operator in symmetric domains},
author = {Farid Bozorgnia},
journal= {arXiv preprint arXiv:1907.13390},
year = {2020}
}