49 citations · 174 across the 33 of their papers we have counts for
46 papers
Hilbert Complexes with Mixed Boundary Conditions -- Part 3: Biharmonic Complexes
Dirk Pauly, Michael Schomburg
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings whi…
Traces for Hilbert Complexes
Ralf Hiptmair, Dirk Pauly, Erick Schulz
We study a new notion of trace operators and trace spaces for abstract Hilbert complexes. We introduce trace spaces as quotient spaces/annihilators. We characterize the kernels and…
Hilbert Complexes with Mixed Boundary Conditions -- Part 2: Elasticity Complex
Dirk Pauly, Michael Schomburg
We show that the elasticity Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings whi…
Hilbert Complexes with Mixed Boundary Conditions -- Part 1: De Rham Complex
Dirk Pauly, Michael Schomburg
We show that the de Rham Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which…
The Index of Some Mixed Order Dirac-Type Operators and Generalised Dirichlet-Neumann Tensor Fields
Dirk Pauly, Marcus Waurick
We revisit a construction principle of Fredholm operators using Hilbert complexes of densely defined, closed linear operators and apply this to particular choices of differential o…
The Elasticity Complex: Compact Embeddings and Regular Decompositions
Dirk Pauly, Walter Zulehner
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/Poincar…