| Abstract: |
| The aim of this talk is to present three convergence results connecting Finsler p-Laplace eigenvalue problems with Cheeger-type constants in the limit as p\to1. After recalling the known asymptotic results for the first Dirichlet eigenvalue, we first address the convergence of the first Robin eigenvalue, using Gamma-convergence to identify the limit as a Finsler Cheeger-type problem in BV. We then turn to the second eigenvalue and eigenfunctions, whose limiting behavior is related to the second Finsler Cheeger constant. Finally, we study a twisted eigenvalue problem and its convergence to the corresponding twisted Finsler Cheeger constant under a volume constraint.
The talk is based on the following works:
[1] R. Barbato, F. Della Pietra, G. Piscitelli, On the first Robin eigenvalue of the Finsler p-Laplace operator as $p\to1$, J. Math. Anal. Appl. 540, 128660 (2024), 1-25.
[2] G. Piscitelli, On the second anisotropic Cheeger constant and related questions, J. Convex Anal. 33.1&2 (2026), 303-324. |
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