Computing the first eigenvalue of the p-Laplacian via the inverse power method.

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.