论文标题
欧几里得空间中的加权Korn和Poincaré-Korn不平等现象
Weighted Korn and Poincaré-Korn inequalities in the Euclidean space and associated operators
论文作者
论文摘要
当它配备满足庞加莱不平等的有限量度并研究相关的自相邻操作员时，我们证明了欧几里得空间的向量领域的功能不平等。加权的Korn不等式比较了差异矩阵，曾经与某些有限维空间进行正交及其对称部分，并以不平等的改进形式的不平等词进行了额外的术语。我们还考虑了使用Witten-Laplace操作员获得的这些不平等的差异矩阵和零级版本的对称部分来估算矢量场投影的庞加尔 - 康恩不平等。常数取决于电势的几何特性，估计值是定量和建设性的。这些不平等是由动力学理论激发的，并且与界面的机械师（1906）（1906）有关。
We prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincaré inequality, and study associated self-adjoint operators. The weighted Korn inequality compares the differential matrix, once projected orthogonally to certain finite-dimensional spaces, with its symmetric part and, in an improved form of the inequality, an additional term. We also consider Poincaré-Korn inequalities for estimating a projection of the vector field by the symmetric part of the differential matrix and zeroth-order versions of these inequalities obtained using the Witten-Laplace operator. The constants depend on geometric properties of the potential and the estimates are quantitative and constructive. These inequalities are motivated by kinetic theory and related with the Korn inequality (1906) in mechanics, on a bounded domain.
