Lions-type compactness and Rubik actions on the Heisenberg group

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 and 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:

24 Oct 2019 08:21

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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