What question did this study set out to answer?

The aim is to explore how the first p-Laplacian eigenvalue behaves as the parameter p becomes very large.

February 22, 2026

The asymptotic behavior of the first Robin eigenvalue with negative parameter as p goes to +∞

Key Points

The aim is to explore how the first p-Laplacian eigenvalue behaves as the parameter p becomes very large.
Investigated the behavior of eigenvalues under Robin boundary conditions
Analyzed the limit of eigenfunctions as p approaches infinity
Established conditions for the resultant eigenfunctions to be viscosity solutions
Proved that the limit of the eigenfunctions is a viscosity solution
Demonstrated the convergence of the first p-Laplacian eigenvalue under specified conditions

Abstract

In this paper, we want to study the asymptotic behavior of the first p-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity solution for the infinity Laplacian eigenvalue problem.

The asymptotic behavior of the first Robin eigenvalue with negative parameter as p goes to +∞

Key Points

Abstract

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