arXiv:2106.03448 Abstract | arXiv Analytics

arXiv:2106.03448 [math.AP]Abstract References Reviews Resources

Hilbert Complexes with Mixed Boundary Conditions: Regular Decompositions, Compact Embeddings, and Functional Analysis ToolBox -- Part 1: De Rham Complex

Published 2021-06-07Version 1

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.

Comments: Key Words: regular potentials, regular decompositions, compact embeddings, Hilbert complexes, Mixed Boundary Conditions, de Rham complex

Categories: math.AP, math-ph, math.FA, math.KT, math.MP

Keywords: mixed boundary conditions, functional analysis toolbox, regular decompositions, compact embeddings, rham complex

Related articles: Most relevant | Search more

arXiv:2108.10792 [math.AP] (Published 2021-08-24)

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

Dirk Pauly, Michael Schomburg

arXiv:2405.04320 [math.AP] (Published 2024-05-07)

Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators

Ivan Gudoshnikov, Michal Křížek

arXiv:2008.08105 [math.AP] (Published 2020-08-18)

On the steady motion of Navier-Stokes flows past a fixed obstacle in a three-dimensional channel under mixed boundary conditions

Gianmarco Sperone