Hörmander向量场的亚椭圆p$ p$ -拉普拉斯谱问题

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-02-17 DOI:10.1002/mana.202300513

Mukhtar Karazym, Durvudkhan Suragan

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引用次数: 0

摘要

基于变分方法，研究了光滑Hörmander向量场引起的次椭圆型p$ p$ -拉普拉斯算子的谱问题。我们推导了最小特征值，证明了它的简单性和孤立性，建立了第一特征函数的正性，并给出了Hölder特征函数对控制距离的正则性。此外，作为副产物，我们确定了L p $L^{p}$ - poincarr - friedrichs不等式对于Hörmander向量场的最佳常数。

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Subelliptic p $p$ -Laplacian spectral problem for Hörmander vector fields

Based on variational methods, we study the spectral problem for the subelliptic $p$ -Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction, and show Hölder regularity of eigenfunctions with respect to the control distance. Moreover, we determine the best constant for the $L^{p}$ -Poincaré–Friedrichs inequality for Hörmander vector fields as a byproduct.

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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