BGG sequences with weak regularity and applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917800198537216 |
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| author | Čap, Andreas Hu, Kaibo |
| author_facet | Čap, Andreas Hu, Kaibo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_01300 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | BGG sequences with weak regularity and applications Čap, Andreas Hu, Kaibo Numerical Analysis Analysis of PDEs Differential Geometry Functional Analysis Representation Theory 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. |
| title | BGG sequences with weak regularity and applications |
| topic | Numerical Analysis Analysis of PDEs Differential Geometry Functional Analysis Representation Theory |
| url | https://arxiv.org/abs/2203.01300 |