05 January 2023

Paper accepted on Applied and Computational Harmonic Analysis

Excited that our paper Nodal domain count for the generalized p-Laplacian – with Piero Deidda and Mario Putti – has been accepted for publication on Applied and Computational Harmonic Analysis. Among the main results, we prove that the eigenvalues of the p-Laplacian on a tree are all variational (and thus they are exactly n), we show that the number of nodal domains of the p-Laplacian for general graphs can be bound both from above and from below, and we deduce that the higher-order Cheeger inequality is tight on trees.