Sharp estimate on the first eigenvalue of the p-Laplacian
By Daniele Valtorta. 2011
95 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5ccb8a30905ee9e92d9a5968fd2b413fdc73ad42
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In Applied Mathematics
- Andrea Mondino
- Fabio Cavalletti
- Ben Andrews
- Guofang Wang
- A. Naber
- Chao Xia
- Daniele Valtorta
- Cristina Trombetti
In Mathematical Physics
- Ben Andrews
- Andrea Mondino
- Fabio Cavalletti
- Guofang Wang
- Chao Xia
- A. Naber
- Daniele Valtorta
- Cristina Trombetti
Citations in the corpus
- An optimal anisotropic Poincaré inequality for convex domains (2011, methodology): “the p-Laplacian in [Valtorta 2012] and to the Laplacian on Alexandrov spaces in [Qian et al.”
- On the critical p-Laplace equation (2022, unknown): “[29]) 1 p Pf (|∇f | ) ≥ 1 n (∆pf) 2 + n n− 1 ( 1 n ∆pf − (p− 1)|∇f | p−4∇2f(∇f,∇f) )2”
- Sharp estimates on the first eigenvalue of the $$p$$p-Laplacian with negative Ricci lower bound (2012, methodology): “(8) We cite from [15] the following version of the Bochner formula.”
- Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds (2015, methodology): “The case K = 0 and the diameter is bounded above was obtained in the sharp form by Valtorta [74].”
- Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations (2014, methodology): “[74] Daniele Valtorta, Sharp estimate on the first eigenvalue of the p-Laplacian, Nonlinear Anal.”
- A remark on optimal weighted Poincar\'e inequalities for convex domains (2012, background): “5) is the optimal estimate already obtained in the unweighted case in [1, 2, 13, 23, 31].”