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 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.

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We introduce an iterative method for computing the first eigenpair (λ p , e p ) for the pLaplacian operator with homogeneous Dirichlet data as the limit of (µ q, u q ) as q → p − , where u q is the positive solution of the sublinear Lane-Emden equation −∆ p u q = µ q u q−1 q with the same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a supersolution which is derived from the solution to the torsional creep problem. Convergence of u q to e p is in the C 1 -norm and the rate of convergence of µ q to λ p is at least O (p − q). Numerical evidence is presented.

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We prove three obstruction results on the existence of equations of state in clusters of stellar systems fulfilling mass-radius relations and some additional bound (on the mass, on the radius or a causal bound). The theorems are proved in great generality. We start with a motivating example of TOV systems and apply our results to stellar systems arising from experimental data.