论文标题
重新审视Rellich的不平等
Revisiting the Rellich inequality
论文作者
论文摘要
我们从隔离径向和球形衍生物的贡献的角度重新审视了雷利希的不平等。这自然会导致比较径向拉普拉斯和拉普拉斯（Beltrami操作员与标准拉普拉斯人）的规范。对于Laplace {Beltrami操作员，三维情况是最微妙的情况，在这里我们通过识别最佳常数来改善Evans和Lewis的结果。我们的论点建立在瓦达德（Wadade）和第二和第三作者最近建立的某些身份以及使用球形谐波的基础上。
We revisit the Rellich inequality from the viewpoint of isolating the contributions from radial and spherical derivatives. This naturally leads to a comparison of the norms of the radial Laplacian and Laplace{Beltrami operators with the standard Laplacian. In the case of the Laplace{ Beltrami operator, the three-dimensional case is the most subtle and here we improve a result of Evans and Lewis by identifying the best constant. Our arguments build on certain identities recently established by Wadade and the second and third authors, along with use of spherical harmonics.
