Asymptotic behavior of the first Robin eigenvalue of nonlinear operators

Rosa Barbato; Francesco Della Pietra; Alba Lia Masiello

Asymptotic behavior of the first Robin eigenvalue of nonlinear operators

Analysis of PDEs 2026-07-27 v1 Optimization and Control Spectral Theory

Authors: Rosa Barbato , Francesco Della Pietra , Alba Lia Masiello

Abstract

Let $\Omega$ be a bounded Lipschitz domain of $\mathbb R^N$ , $N\geq 2$ . In this paper, we study the asymptotic behavior of the first Robin eigenvalue of the $p$ -Laplace operator as $\beta$ goes to $0$ and as $\beta$ goes to $+\infty$ , deriving sharp asymptotic expansions of the eigenvalue; the expansion in the Dirichlet limit $\beta\to+\infty$ is obtained under the additional assumption that $\partial\Omega$ is of class $C^{1,1}$ .

Keywords

robin eigenvalue p-laplace operator asymptotic expansion dirichlet limit lipschitz domain

Cite

@article{arxiv.2607.24488,
  title  = {Asymptotic behavior of the first Robin eigenvalue of nonlinear operators},
  author = {Rosa Barbato and Francesco Della Pietra and Alba Lia Masiello},
  journal= {arXiv preprint arXiv:2607.24488},
  year   = {2026}
}