Asymptotic behavior of the first Robin eigenvalue of nonlinear operators

2026/07/27 by Rosa Barbato, Francesco Della Pietra, Alba Lia Masiello
Mathematics · #math.AP #math.OC #math.SP

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Abstract

Let Ω be a bounded Lipschitz domain of \mathbb R^N, N≥ 2. In this paper, we study the asymptotic behavior of the first Robin eigenvalue of the p-Laplace operator as β goes to 0 and as β goes to +∞, deriving sharp asymptotic expansions of the eigenvalue; the expansion in the Dirichlet limit β→+∞ is obtained under the additional assumption that ∂Ω is of class C^1,1.

Citations

• Asymptotics of nonlinear Robin energies
• Upper and lower bounds for the first Robin eigenvalue of nonlinear elliptic operators
• On asymptotics of Robin eigenvalues in the Dirichlet limit
• The Robin Laplacian in the large coupling limit: Convergence and\n spectral asymptotic
• Boundary regularity for solutions of degenerate elliptic equations

Related

• Upper and lower bounds for the first Robin eigenvalue of nonlinear elliptic operators
• On the eigenvalues of the Robin Laplacian with a complex parameter
• Higher Robin eigenvalues for the p-Laplacian operator as p approaches 1
• The asymptotic behavior of the first Robin eigenvalue with negative parameter as p goes to +∞
• On asymptotics of Robin eigenvalues in the Dirichlet limit