Hilbert Complexes with Mixed Boundary Conditions -- Part 1: De Rham Complex

Abstract

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. Higher Sobolev order results are proved as well.

arXiv commentKey Words: Hilbert complexes, mixed boundary conditions, de Rham complex, compact embeddings, regular potentials, regular decompositions

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• Hilbert Complexes with Mixed Boundary Conditions -- Part 2: Elasticity Complex
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