The elasticity complex: compact embeddings and regular decompositions

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Dirk Pauly - , Institut für Analysis (Autor:in)
  • Walter Zulehner - , Österreichische Akademie der Wissenschaften (Autor:in)

Abstract

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)4393-4421
Seitenumfang29
Fachzeitschrift Applicable analysis : an international journal
Jahrgang102
Ausgabenummer16
Frühes Online-DatumSept. 2022
PublikationsstatusVeröffentlicht - 2 Nov. 2023
Peer-Review-StatusJa

Externe IDs

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

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

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