Dirk Pauly: On some Hilbert complexes, related compact embeddings, and the div-curl lemma
Speaker: Dirk Pauly (Universität Duisburg-Essen)
Title: On some Hilbert complexes, related compact embeddings, and the div-curl lemma
Abstract: We investigate some Hilbert complexes, i.e., the classical de Rham complex, the elasticity complex, and the biharmonic complex. 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).