Abstract
In this paper, we prove an upper bound for the first Robin eigenvalue of the p-Laplacian with a positive boundary parameter and a quantitative version of the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the p-Laplacian with negative boundary parameter, among convex sets with prescribed perimeter. The proofs are based on a comparison argument obtained by means of inner sets, introduced by Payne, Weinberger [32] and Pólya [33].
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