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Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls

Boundary Value Problems volume 2010, Article number: 690342 (2010) Cite this article

Abstract

For one-dimensional -Laplacian with weights in balls, we are interested in the extremal values of the th positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values are given by some best Sobolev constants.

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  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Ping Yan

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  1. Ping Yan
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Correspondence to Ping Yan.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yan, P. Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls. Bound Value Probl 2010, 690342 (2010). https://doi.org/10.1155/2010/690342

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  • DOI: https://doi.org/10.1155/2010/690342

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