A Sharp estimate for the first Robin–Laplacian eigenvalue with negative boundary parameter
A Sharp estimate for the first Robin–Laplacian eigenvalue with negative boundary parameter
In this paper we prove that the ball maximizes the first eigenvalue of the Robin Laplacian operator with negative boundary parameter, among all convex sets of Rn with prescribed perimeter. The key of the proof is a dearrangement procedure of the first eigenfunction of the ball on the level sets …