AI 中文总结
本文针对具快速振荡$L^q$权的$p$-拉普拉斯算子，分析其变分特征值的收敛速率，推导了含特征值指标$k$和振荡参数$\varepsilon$的显式估计，涵盖两类边界条件，扩展了已有文献结果。
AI 中文摘要
本文研究具快速振荡权且属于合适$L^q$空间的势的$p$-拉普拉斯算子的变分特征值的收敛速率。我们的分析涵盖Dirichlet和Neumann边界条件，并根据特征值指标$k \in \mathbb{N}$和振荡参数$\varepsilon > 0$推导显式估计。这些结果通过对某些振荡积分的详细考察获得，扩展了文献中先前已知的结果。
英文摘要
In this article, we study the convergence rates of variational eigenvalues of the $p$-Laplacian with rapidly oscillating weights and potentials belonging in a suitable $L^q$ space. Our analysis covers both Dirichlet and Neumann boundary conditions, and we derive explicit estimates in terms of the eigenvalue index $k \in \mathbb{N}$ and the oscillation parameter $\varepsilon > 0$. These results are obtained through a detailed examination of certain oscillatory integrals and extend previously known results in the literature.
Commentsto appear in Mathematische Nachrichten
