English

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 pp-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 LpL^p-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}
}