Spectral stability of the pp-Laplacian

We study the dependence of the eigenvalues of the pp-Laplacian upon domain perturbation. We prove Lipschitz-type estimates for the deviation of the eigenvalues following a domain perturbation. Such estimates are expressed in terms of suitable measures of vicinity between open sets, such as the ‘atlas distance’ and the ‘lower Hausdorff–Pompeiu deviation’. In the case of open sets with Hölder continuous boundaries, our results improve a result known for the first eigenvalue.