Year: 2022
Type: preprint
Abstract: We investigate some Bernstein-Gelfand-Gelfand (BGG) complexes on bounded Lipschitz domains in $\mathbb{R}^n$ consisting of Sobolev spaces. In particular, we compute the cohomology of the conformal deformation complex and the conformal Hessian complex in the Sobolev setting. The machinery does not require algebraic injectivity/surjectivity conditions between the input spaces, and allows multiple input complexes. As applications, we establish a conformal Korn inequality in two space dimensions with the Cauchy-Riemann operator and an additional third order operator with a background in Möbius geometry. We show that the linear Cosserat elasticity model is a Hodge-Laplacian problem of a twisted de-Rham complex. From this cohomological perspective, we propose potential generalizations of continuum models with microstructures.
Source: arXiv (Cornell University)
Authors: Čap, Andreas, Hu, Kaibo
Institution: University of Oxford
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
Award: G5797020563
OpenAlex ID: W4221142282