The Inverse Power Method for the p(x)-Laplacian Problem

We present an inverse power method for the computation of the first homogeneous eigenpair of the p(x)-Laplacian problem. The operators are discretized by the finite element method. The inner minimization problems are solved by a globally convergent inexact Newton method. Numerical comparisons are made, in one- and two-dimensional domains, with other results present in literature for the constant case p(x)=p and with other minimization techniques (namely, the nonlinear conjugate gradient) for the p(x) variable case.