| Issue |
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
|---|---|---|
| Article Number | S23 | |
| Number of page(s) | 16 | |
| DOI | https://doi.org/10.1051/cocv/2020079 | |
| Published online | 01 March 2021 | |
A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter
1
Universitá del Salento, Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Via per Arnesano,
73100
Lecce, Italy.
2
University of Jyväskylä, Department of Mathematics and Statistics,
P.O. Box 35 (MaD),
40014,
Jyväskylä, Finland.
* Corresponding author: simone.cito@unisalento.it; domenico.a.lamanna@jyu.fi
Received:
26
May
2020
Accepted:
12
November
2020
The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalue λβ with negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer for λβ and the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.
Mathematics Subject Classification: 35P15 / 35B35 / 49Q10 / 49R05
Key words: Robin eigenvalue / quantitative isoperimetric inequality / convex sets
© EDP Sciences, SMAI 2021
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.