Approximation of the second eigenvalue of the $p$-Laplace operator in symmetric domains

Farid Bozorgnia

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arXiv · 1907.13390

Approximation of the second eigenvalue of the $p$-Laplace operator in symmetric domains

Farid Bozorgnia

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Abstract

A new idea to approximate the second eigenfunction and the second eigenvalue of $p$-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 $L^p$-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.

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BibTeX RIS

Farid Bozorgnia. 2019-07-31. Approximation of the second eigenvalue of the $p$-Laplace operator in symmetric domains. https://arxiv.org/abs/1907.13390

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