The inclusion of Stekloff eigenvalues for nonsmooth bounded domains (Q1338338)

The author presents numerical evaluations of eigenvalue \(p\) of the problem \(\Delta u = 0\) in a bounded domain \(G\) of \(\mathbb{R}^2\), \(\partial_nu = pu\) on the piecewise analytic boundary \(\partial G\) based on the theorem of Kryloff and Bogoljubow ensuring the existence of an eigenvalue \(p\) with \(|p - p_* |\leq |\partial_n u_* - p_* u_* |_{\partial G} |u_* |^{- 1}_{\partial G}\), where the trial function \(u_* \in C^2 (\overline G)\) is harmonic and \(p_*\) is a real number, and on the use of trial functions adapted to the shape of the domain.