## 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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### References:

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