Mixed Eigenvalues of {\LARGE $\pmb p$\,}-Laplacian

Mu-Fa Chen; Ling-Di Wang; Yu-Hui Zhang

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arXiv · 1501.03228

Mixed Eigenvalues of {\LARGE $\pmb p$\,}-Laplacian

Mu-Fa Chen·Ling-Di Wang·Yu-Hui Zhang

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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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BibTeX RIS

Mu-Fa Chen, Ling-Di Wang, Yu-Hui Zhang. 2015-01-14. Mixed Eigenvalues of {\LARGE $\pmb p$\,}-Laplacian. https://arxiv.org/abs/1501.03228

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