Hilbert Complexes with Mixed Boundary Conditions -- Part 1: De Rham Complex
Analysis of PDEs
2022-03-14 v6 Mathematical Physics
Functional Analysis
K-Theory and Homology
math.MP
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.
Cite
@article{arxiv.2106.03448,
title = {Hilbert Complexes with Mixed Boundary Conditions -- Part 1: De Rham Complex},
author = {Dirk Pauly and Michael Schomburg},
journal= {arXiv preprint arXiv:2106.03448},
year = {2022}
}
Comments
Key Words: Hilbert complexes, mixed boundary conditions, de Rham complex, compact embeddings, regular potentials, regular decompositions