论文标题
Korn在各向异性Sobolev空间中的不平等
Korn's inequality in anisotropic Sobolev spaces
论文作者
论文摘要
自20世纪初首次出现以来，Korn的不平等是令人兴奋的研究的核心。许多不平等的应用是连续力学中各种各样问题的分析和构建。在本文中，我们证明了经典的Korn不等式在{\ It Anisotropic Sobolev spaces}中成立。我们还证明，涉及非线性连续图的Korn不平等的扩展在此类空间中是有效的。最后，我们指出，Poincare的不平等现象也存在于各向异性的Sobolev空间中。
Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large variety of problems in continuum mechanics. In this paper, we prove that the classical Korn inequality holds true in {\it anisotropic Sobolev spaces}. We also prove that an extension of Korn's inequality, involving non-linear continuous maps, is valid in such spaces. Finally, we point out that another classical inequality, Poincare's inequality, also holds in anisotropic Sobolev spaces.
