On boundary value problems for some conformally invariant differential operators

Möllers J, Ørsted B, Zhang G (2016)

Publication Status: Published

Publication Type: Journal article

Publication year: 2016

Journal

Communications in Partial Differential Equations

Book Volume: 41

Pages Range: 609-643

Journal Issue: 4

DOI: 10.1080/03605302.2015.1123275

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.

Authors with CRIS profile

Jan Frahm Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Aarhus University

Denmark (DK) Chalmers University of Technology / Chalmers tekniska högskola

Sweden (SE)

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.

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