An Inequality Between Dirichlet and Neumann Eigenvalues of the Heisenberg Laplacian
Anders Hansson · Communications in Partial Differential Equations · 2008
Let λ k and μ k be the eigenvalues of the Dirichlet and Neumann problems, respectively, in a domain of finite measure in ℝ d , d > 1. Filonov has proved in a simple way that the inequality μ k+1 < λ k holds for the Laplacian. We extend his result to the Heisenberg Laplacian in three-dimensional domains which fulfill certain geometric conditions.