Computing the first eigenvalue of the p-Laplacian via the inverse power method |
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Authors: | Rodney Josué Biezuner Grey Ercole |
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Institution: | Departamento de Matemática - ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Caixa Postal 702, 30161-970, Belo Horizonte, MG, Brazil |
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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 |
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