Bounded Poincar\'e operators for twisted and BGG complexes
Numerical Analysis
2023-11-17 v2 Numerical Analysis
Analysis of PDEs
Functional Analysis
Abstract
We construct bounded Poincar\'e operators for twisted complexes and BGG complexes with a wide class of function classes (e.g., Sobolev spaces) on bounded Lipschitz domains. These operators are derived from the de Rham versions using BGG diagrams and, for vanishing cohomology, satisfy the homotopy identity in degrees . The operators preserve polynomial classes if the de Rham versions do so.
Cite
@article{arxiv.2304.07185,
title = {Bounded Poincar\'e operators for twisted and BGG complexes},
author = {Andreas Čap and Kaibo Hu},
journal= {arXiv preprint arXiv:2304.07185},
year = {2023}
}
Comments
published in J. Math. Pures Appl. DOI: 10.1016/j.matpur.2023.09.008