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

2019/07/31 by Farid Bozorgnia, Bozorgnia, Farid · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Approximation and Integration #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1907.13390

openalex publication_date 2019/07/31 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28

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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