Balogh, Zoltán M.; Kristály, Alexandru (2013). Lions-type compactness and Rubik actions on the Heisenberg group. Calculus of variations and partial differential equations, 48(1-2), pp. 89-109. Springer 10.1007/s00526-012-0543-y
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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 TeX 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 TeX. 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.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Balogh, Zoltan, Kristaly, Alexandru |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0944-2669 |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Mario Amrein |
Date Deposited: |
03 Jun 2014 09:37 |
Last Modified: |
05 Dec 2022 14:28 |
Publisher DOI: |
10.1007/s00526-012-0543-y |
BORIS DOI: |
10.7892/boris.41972 |
URI: |
https://boris.unibe.ch/id/eprint/41972 |
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