Hilbert complexes with mixed boundary conditions part 1: de Rham complex
Dirk Pauly, Michael Schomburg
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.
Topics & Concepts
MathematicsLipschitz continuitySobolev spaceBoundary (topology)Bounded functionPure mathematicsHilbert spaceMathematical analysisOrder (exchange)Sobolev spaces for planar domainsFunctional analysisInterpolation spaceFinanceEconomicsGeneChemistryBiochemistryAdvanced Mathematical Physics ProblemsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in Engineering