与变号容度测度相关的 $p$-拉普拉斯算子高阶特征值的优化结果
偏微分方程分析
2021-01-20 v2 最优化与控制
谱理论
摘要
本文证明了：在包含于有限测度盒中、固定测度的 -拟开集族中，最小化 -拉普拉斯算子第 变分特征值的最优集之存在性。对于与 Schrödinger 势相关的 -拉普拉斯算子特征值，也得到了类似的存在性结果。为处理这些非线性形状优化问题，我们发展了一种通用方法，能够处理在 -收敛下与变号容度测度相关的 -拉普拉斯算子特征值对连续变化的依赖关系。
引用
@article{arxiv.1905.09563,
title = {Optimization results for the higher eigenvalues of the $p$-Laplacian associated with sign-changing capacitary measures},
author = {Marco Degiovanni and Dario Mazzoleni},
journal= {arXiv preprint arXiv:1905.09563},
year = {2021}
}
备注
This is an extended version of the published paper (on J. London Math. Soc.). In particular, the reader can find an extended Section 2 of preliminaries and the detailed proofs of Theorem 3.1, Proposition 5.9 and Corollary 5.26, which have been omitted or shortened in the published version. The numbering of Sections, Theorems, Lemmas, etc is unchanged