The aim of this paper is to prove the sharp estimate on the first nontrivial eigenvalue of the p-Laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and to characterize the equality case. The estimate applies to manifolds with empty or convex boundary, and in this latter case we also assume Neumann boundary conditions for the p-Laplacian. The main tool used for the proof is a gradient comparison based on a generalized p-Bochner formula.

Valtorta, D. (2012). Sharp estimate on the first eigenvalue of the p-Laplacian. NONLINEAR ANALYSIS, 75(13), 4974-4994 [10.1016/j.na.2012.04.012].

Sharp estimate on the first eigenvalue of the p-Laplacian

Valtorta, D
2012

Abstract

The aim of this paper is to prove the sharp estimate on the first nontrivial eigenvalue of the p-Laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and to characterize the equality case. The estimate applies to manifolds with empty or convex boundary, and in this latter case we also assume Neumann boundary conditions for the p-Laplacian. The main tool used for the proof is a gradient comparison based on a generalized p-Bochner formula.
Articolo in rivista - Articolo scientifico
Convex boundary; First eigenvalue; Nonnegative Ricci curvature; p-Laplacian;
English
2012
75
13
4974
4994
open
Valtorta, D. (2012). Sharp estimate on the first eigenvalue of the p-Laplacian. NONLINEAR ANALYSIS, 75(13), 4974-4994 [10.1016/j.na.2012.04.012].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/393679
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