@article{388ac643-51c6-4cf7-aad3-30c8ea701bb7,
  abstract     = {{<p>Inequalities between Dirichlet and Neumann eigenvalues of the Laplacian and of other differential operators have been intensively studied in the past decades. The aim of this paper is to introduce differential forms and the de Rham complex in the study of such inequalities. We show how differential forms lie hidden at the heart of the work of Rohleder on inequalities between Dirichlet and Neumann eigenvalues for the Laplacian on planar domains. Moreover, we extend the ideas of Rohleder to a new proof of Friedlander’s inequality for any bounded Lipschitz domain.</p>}},
  author       = {{Fries, Magnus and Goffeng, Magnus and Miranda, Germán}},
  issn         = {{1664-039X}},
  keywords     = {{de Rham complex; differential forms; Dirichlet Laplacian; eigenvalues inequalities; Friedlander’s inequality; Neumann Laplacian}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{4}},
  pages        = {{1593--1613}},
  publisher    = {{European Mathematical Society Publishing House}},
  series       = {{Journal of Spectral Theory}},
  title        = {{Reproving Friedlander’s inequality with the de Rham complex}},
  url          = {{http://dx.doi.org/10.4171/JST/582}},
  doi          = {{10.4171/JST/582}},
  volume       = {{15}},
  year         = {{2025}},
}