On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍ n

IF 0.9 3区数学 Q2 MATHEMATICS Analysis and Geometry in Metric Spaces Pub Date : 2024-08-29 DOI:10.1515/agms-2024-0006

Sihua Liang, Patrizia Pucci, Yueqiang Song, Xueqi Sun

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Abstract

This article is devoted to the study of a critical Choquard-Kirchhoff

-sub-Laplacian equation on the entire Heisenberg group

H n

{{\mathbb{H}}}^{n}

, where the Kirchhoff function

can be zero at zero, i.e., the equation can be degenerate, and involving a nonlinearity, which is critical in the sense of the Hardy-Littlewood-Sobolev inequality. We first establish the concentration-compactness principle for the

-sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.

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关于ℍ n 中的临界 Choquard-Kirchhoff p-sub-Laplacian 方程

本文致力于研究整个海森堡群 H n {{mathbb{H}}}^{n} 上的临界乔夸德-基尔霍夫 p p -次拉普拉斯方程。，其中基尔霍夫函数 K K 在零点可能为零，即方程可能是退化的，并且涉及非线性，在哈代-利特尔伍德-索博列夫不等式的意义上是临界的。我们首先建立了海森堡群上 p p-子拉普拉奇乔夸德方程的集中-紧凑性原理，然后证明了存在性结果。

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

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.

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