Lions-type compactness and Rubik actions on the Heisenberg group |
| |
Authors: | Zoltán M Balogh Alexandru Kristály |
| |
Institution: | 1. Mathematisches Institut, Universit?t Bern, Sidlerstrasse 5, 3012, Bern, Switzerland 2. Department of Economics, Babe?-Bolyai University, 400591, Cluj-Napoca, Romania
|
| |
Abstract: | 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 ${\mathbb{H}^n=\mathbb{C}^n \times \mathbb{R}}$ is provided by the unitary group U(n) × {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 ${HW_0^{1,2}(\mathbb{H}^n)}$ . 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) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|