English

Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width

Spectral Theory 2024-03-29 v4 Mathematical Physics Analysis of PDEs math.MP

Abstract

We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.

Keywords

Cite

@article{arxiv.2305.11799,
  title  = {Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width},
  author = {Corentin Léna and Jonathan Rohleder},
  journal= {arXiv preprint arXiv:2305.11799},
  year   = {2024}
}

Comments

18 pages, 1 figure. Minor edits and updated list of references. To appear in "Analysis and Mathematical Physics"