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The first eigenfunctions and eigenvalue of the p-Laplacian on Finsler manifolds

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Abstract

This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C 1,α. Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature, on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Tongling University, Tongling, 244000, China

    SongTing Yin

  2. School of Mathematical Sciences, Tongling University, Shanghai, 200092, China

    Qun He

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  1. SongTing Yin
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  2. Qun He
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Correspondence to Qun He.

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Yin, S., He, Q. The first eigenfunctions and eigenvalue of the p-Laplacian on Finsler manifolds. Sci. China Math. 59, 1769–1794 (2016). https://doi.org/10.1007/s11425-015-0411-9

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  • DOI: https://doi.org/10.1007/s11425-015-0411-9

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