一般向量场的$p$-子拉普拉斯算子的主频率

arXiv: Analysis of PDEs Pub Date : 2020-08-13 DOI:10.4171/ZAA/1674

Michael Ruzhansky, Bolys Sabitbek, D. Suragan

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引用次数: 2

摘要

本文证明了一般向量场的Dirichlet p-sub-Laplacian的主频率(或第一特征值)的唯一性和简单性。作为一个副产品，我们建立了Caccioppoli不等式，并讨论了Grushin平面和Heisenberg群上的特殊情况。

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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Principal Frequency of $p$-Sub-Laplacians for General Vector Fields

In this paper, we prove the uniqueness and simplicity of the principal frequency (or the first eigenvalue) of the Dirichlet p-sub-Laplacian for general vector fields. As a byproduct, we establish the Caccioppoli inequalities and also discuss the particular cases on the Grushin plane and on the Heisenberg group.

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arXiv: Analysis of PDEs

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