论文标题
BGG序列的规律性较弱和应用
BGG sequences with weak regularity and applications
论文作者
论文摘要
我们研究了$ \ mathbb {r}^n $由Sobolev空间组成的$ \ Mathbb {r}^n $中的一些Bernstein-Gelfand-Gelfand（BGG）复合物。特别是，我们计算了Sobolev设置中的形成型复合物和保形Hessian复合物的共同体。该机械不需要输入空间之间的代数注射率/过冲条件，并且允许多个输入复合物。作为应用程序，我们在两个空间维度上建立了一个与Cauchy-Riemann运算符和具有Möbius几何背景背景的其他三阶操作员的共形korn不平等。我们表明，线性cosserat弹性模型是扭曲的de-rham综合体的霍奇 - 拉普拉斯问题。从这个同一个学的角度来看，我们提出了具有微观结构的连续模型的潜在概括。
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.
