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Mixed eigenvalues of p-Laplacian

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Abstract

The mixed principal eigenvalue of p -Laplacian (equivalently, the optimal constant of weighted Hardy inequality in L p space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Mu-Fa Chen, Lingdi Wang & Yuhui Zhang

  2. School of Mathematics and Information Sciences, Henan University, Kaifeng, 475004, China

    Lingdi Wang

Authors
  1. Mu-Fa Chen
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  2. Lingdi Wang
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  3. Yuhui Zhang
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Correspondence to Lingdi Wang.

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Chen, MF., Wang, L. & Zhang, Y. Mixed eigenvalues of p-Laplacian. Front. Math. China 10, 249–274 (2015). https://doi.org/10.1007/s11464-015-0375-0

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  • DOI: https://doi.org/10.1007/s11464-015-0375-0

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