Volume 27, 2021Regular 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
|Number of page(s)||16|
|Published online||01 March 2021|
A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter
Universitá del Salento, Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Via per Arnesano,
2 University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), 40014, Jyväskylä, Finland.
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
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