The elasticity complex: compact embeddings and regular decompositions

Research output: Contribution to journalResearch articleContributedpeer-review



We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincaré type estimates, Helmholtz-type decompositions, regular decompositions, regular potentials, finite cohomology groups, and, most importantly, new compact embedding results. Our results hold for general bounded strong Lipschitz domains of arbitrary topology and rely on a general functional analysis framework (FA-ToolBox). Moreover, we present a simple technique to prove the compact embeddings based on regular decompositions/potentials and Rellich's selection theorem, which can be easily adapted to any Hilbert complex.


Original languageEnglish
Pages (from-to)4393-4421
Number of pages29
Journal Applicable analysis : an international journal
Issue number16
Early online dateSept 2022
Publication statusPublished - 2 Nov 2023

External IDs

WOS 000854465400001
Mendeley bf1468cf-2710-359b-8044-3734101994ec
Scopus 85138300400
ORCID /0000-0003-4155-7297/work/153109783


ASJC Scopus subject areas


  • cohomology groups, compact embeddings, elasticity complex, Friedrichs/Poincaré type estimates, Helmholtz decompositions, Hilbert complexes, regular decompositions