论文标题
Korn-Maxwell-Sobolev的不平等不平等，一般不兼容
Korn-Maxwell-Sobolev inequalities for general incompatibilities
论文作者
论文摘要
在尖锐的标准下，我们建立了一个针对超线性生长制度中普遍不相容领域的强制性Korn型不平等的家族。这扩展并统一了几种以前已知的不平等现象，这些不平等与存在理论有关，以最佳方式在连续机械中的多种模型中至关重要。不同于我们的上一件工作（ARXIV 2206.10373），我们专注于$ p = 1 $和由矩阵卷发控制的情况，本文中考虑的案例$ p> 1 $使我们能够从谐波分析中获得更强大的结果，但相反，它可以访问更多的一般性不足。尤其是，在最后两位作者和Müller（Calc。Var。Pde60（2021），150，150）中，我们获得了最近证明的不平等现象的急剧概括，并在不兼容的KORN型不平等现象的领域中具有相互恒定的脱位能量。但是，也适用于高阶方案，我们的方法同样赋予了涉及Kröner不合理性张量$ \ MATHRM {INC} $的第一个和尖锐的不平等现象。
We establish a family of coercive Korn-type inequalities for generalised incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the existence theory for a multitude of models in continuum mechanics in an optimal way. Different from our preceding work (ArXiv 2206.10373), where we focussed on the case $p=1$ and incompatibilities governed by the matrix curl, the case $p>1$ considered in the present paper gives us access to substantially stronger results from harmonic analysis but conversely deals with more general incompatibilities. Especially, we obtain sharp generalisations of recently proved inequalities by the last two authors and Müller (Calc. Var. PDE 60 (2021), 150) in the realm of incompatible Korn-type inequalities with conformally invariant dislocation energy. However, being applicable to higher order scenarios as well, our approach equally gives the first and sharp inequalities involving Kröner's incompability tensor $\mathrm{inc}$.
