Mixed eigenvalues of p-Laplacian

作者：Chen, Mu-Fa; Wang, Lingdi^*; Zhang, Yuhui

来源：Frontiers of Mathematics in China, 2015, 10(2): 249-274.

DOI：10.1007/s11464-015-0375-0

• p-Laplacian
• Hardy inequality in L-p space
• mixed boundaries
• explicit estimates
• eigenvalue
• approximating procedure

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.

• 出版日期2015-4
• 单位北京师范大学; 河南大学