Mixed Eigenvalues of {\LARGE $\pmb p$\,}-Laplacian
Spectral Theory
2015-01-15 v1 Analysis of PDEs
Probability
Abstract
The mixed principal eigenvalue of -Laplacian (equivalently, the optimal constant of weighted Hardy inequality in 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.
Cite
@article{arxiv.1501.03228,
title = {Mixed Eigenvalues of {\LARGE $\pmb p$\,}-Laplacian},
author = {Mu-Fa Chen and Ling-Di Wang and Yu-Hui Zhang},
journal= {arXiv preprint arXiv:1501.03228},
year = {2015}
}
Comments
25 pages, 2 figures in Front. Math. China 2015