论文标题
曲率的几何非线性平坦cosserat微极膜壳的规律性
Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature
论文作者
论文摘要
我们考虑严格衍生的薄壳膜$γ$ - 限制了三维各向同性的几何学上非线性的cosserat微极模型，并推断出两个中表面变形$ m：ω\ subset {\ subbb r}^2 \ to { $ r：ω\ subset {\ mathbb r}^2 \ to so（3）$。唯一的另一个结构假设是，曲率能量仅取决于Uni-Contant各向同性dirichlet型能量项$ | dr |^2 $。我们为系统使用Rivière的谐波地图类型系统的规律性技术，该技术将谐波图与$（3）$与$ M $的线性方程式相结合。谐波图方程中的附加耦合项是至关重要的一致性，只能由于其特殊结构而进行处理。
We consider the rigorously derived thin shell membrane $Γ$-limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation $m:ω\subset{\mathbb R}^2\to{\mathbb R}^3$ and the orthogonal microrotation tensor field $R:ω\subset{\mathbb R}^2\to SO(3)$. The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet type energy term $|DR|^2$. We use Rivière's regularity techniques of harmonic map type systems for our system which couples harmonic maps to $SO(3)$ with a linear equation for $m$. The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure.
