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.

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

References in corpus (3)

• Complexes from complexes
• The Elasticity Complex: Compact Embeddings and Regular Decompositions
• The Index of Some Mixed Order Dirac-Type Operators and Generalised Dirichlet-Neumann Tensor Fields

Cited by in corpus (3)

• Hilbert Complexes with Mixed Boundary Conditions -- Part 2: Elasticity Complex
• A global higher regularity result for the static relaxed micromorphic model on smooth domains
• Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains