Computing the first eigenvalue of the p-Laplacian via the inverse power method.
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Date
2009
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Abstract
In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square.
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Keywords
p-Laplacian, First eigenvalue, Comparison principle, Power method
Citation
BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 2012