Eigenvalue Homogenization for the p $p$ -Laplacian With Rapidly Oscillating L q $L^q$ Weights

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-10-05 Epub Date: 2026-08-21 DOI:10.1002/mana.70231

Ariel Salort

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引用次数: 0

Abstract

In this paper, 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 $k \in N$ and the oscillation parameter $ε > 0$ . These results are obtained through a detailed examination of certain oscillatory integrals and extend previously known results in the literature.

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具有快速振荡lq $L^q$权值的p$ p$ -拉普拉斯算子的特征值均匀化

本文研究了在合适的lq $L^q$空间中具有快速振荡权和势的p$ p$ -拉普拉斯算子的变分特征值的收敛速率。我们的分析涵盖了Dirichlet和Neumann边界条件，并且我们推导出了特征值指标k∈N $k \in \mathbb {N}$和振荡参数ε >； 0$ \varepsilon > 0$的显式估计。这些结果是通过对某些振荡积分的详细检查获得的，并扩展了文献中先前已知的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index