English

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

Spectral Theory 2015-01-15 v1 Analysis of PDEs Probability

Abstract

The mixed principal eigenvalue of pp\,-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in LpL^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.

Keywords

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

R2 v1 2026-06-22T08:00:38.887Z