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Vincenzo Amato

Publications and source records attributed to Vincenzo Amato.

20 records · Page 2Linked to original sources

arXiv2022

Estimates for Robin $p$-Laplacian eigenvalues of convex sets with prescribed perimeter

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, Weimberger and Polya.

math.AP↗

arXiv2021

Comparison results for solutions to p-Laplace equations with Robin boundary conditions

In the last decades comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the results obtained in arXiv:1909.11950 to the case of p-Laplace operator with Robin boundary conditions. The point-wise comparison, obtained in arXiv:1909.11950 only in the planar case, holds true in any dimension if p is sufficiently small.

math.AP↗