On boundary value problems for some conformally invariant differential operators

Journal article


Publication Details

Author(s): Möllers J, Ørsted B, Zhang G
Journal: Communications in Partial Differential Equations
Publication year: 2016
Volume: 41
Journal issue: 4
Pages range: 609-643
ISSN: 1532-4133


Abstract


We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace, respectively, Heisenberg subgroup. These operators are shown to be self-adjoint in certain Sobolev type spaces and the related boundary value problems are proven to have unique solutions in these spaces. We further find the corresponding Poisson transforms explicitly in terms of their integral kernels and show that they are isometric between Sobolev spaces and extend to bounded operators between certain L-spaces. The conformal invariance of the differential operators allows us to apply unitary representation theory of reductive Lie groups, in particular recently developed methods for restriction problems.



FAU Authors / FAU Editors

Frahm, Jan Prof. Dr.
Juniorprofessur für Lie-Theorie/Darstellungstheorie


External institutions with authors

Aarhus University
Chalmers University of Technology / Chalmers tekniska högskola


How to cite

APA:
Möllers, J., Ørsted, B., & Zhang, G. (2016). On boundary value problems for some conformally invariant differential operators. Communications in Partial Differential Equations, 41(4), 609-643. https://dx.doi.org/10.1080/03605302.2015.1123275

MLA:
Möllers, Jan, Bent Ørsted, and Genkai Zhang. "On boundary value problems for some conformally invariant differential operators." Communications in Partial Differential Equations 41.4 (2016): 609-643.

BibTeX: 

Last updated on 2018-16-11 at 13:50