Lions-type compactness and Rubik actions on the Heisenberg group

被引：25

作者：

Balogh, Zoltan M. ^{[1
]}

Kristaly, Alexandru ^{[2
]}

机构：

[1] Univ Bern, Math Inst, CH-3012 Bern, Switzerland

[2] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 48卷 / 1-2期

基金：

瑞士国家科学基金会;

关键词：

SYMMETRIC CRITICALITY; EXISTENCE; PRINCIPLE; EQUATION; THEOREM; SPACES;

D O I：

10.1007/s00526-012-0543-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group is provided by the unitary group U(n) x {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein's horizontal Sobolev space . As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) x {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

引用

页码：89 / 109

页数：21

共 23 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2] Polar coordinates in Carnot groups [J].