Hilbert Complexes with Mixed Boundary Conditions: Regular Decompositions, Compact Embeddings, and Functional Analysis ToolBox -- Part 1: De Rham Complex Article Swipe
Related Concepts
Lipschitz continuity
Mathematics
Boundary (topology)
Pure mathematics
Bounded function
Toolbox
Mathematical analysis
Algebra over a field
Computer science
Programming language
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 follow by abstract arguments using functional analysis together with particular regular decompositions.
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