An inequality à la Szegő-Weinberger for the \(p-\)Laplacian on convex sets

An inequality à la Szegő-Weinberger for the \(p-\)Laplacian on convex sets

In this paper we prove a sharp inequality of Szegő-Weinberger type for the first nontrivial eigenvalue of the \(p-\)Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants, extensions and limit cases are investigated as well.

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Veröffentlicht in:arXiv.org 2015-08
Hauptverfasser: Brasco, L, Nitsch, C, Trombetti, C
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Convexity
Eigenvalues
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Zusammenfassung:In this paper we prove a sharp inequality of Szegő-Weinberger type for the first nontrivial eigenvalue of the \(p-\)Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants, extensions and limit cases are investigated as well.
ISSN:2331-8422