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Computing the first eigenvalue of the \(p\)-Laplacian via the inverse power method. (English) Zbl 1172.35047

Authors’ abstract: The authors 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 \({\mathbb R}^n\) 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.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
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