The Elasticity Complex
Prof. Dirk PaulyMarch 14, 2019, 3:30 p.m. S2 416-1
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For these tensor fields we show closed ranges, Friedrichs/Poincare 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).