Revisiting the Rellich inequality
Revisiting the Rellich inequality
复制标题
DOI：
10.1007/s00209-022-03203-4
复制
发表时间：
2022-09
影响因子：
0.8
通讯作者：
N. Bez;Shuji Machihara;T. Ozawa
中科院分区：
文献类型：
--
作者：
N. Bez;Shuji Machihara;T. Ozawa
我们从隔离径向导数和球面导数的贡献的角度重新审视雷利希不等式。这自然会导致将径向拉普拉斯算子和拉普拉斯-贝尔特拉米算子的范数与标准拉普拉斯算子进行比较。在拉普拉斯-贝尔特拉米算子的情况下，三维情况是最微妙的，在这里我们通过识别最佳常数来改进埃文斯和刘易斯的结果。我们的论点建立在瓦达德以及第二和第三作者最近建立的某些恒等式以及球谐函数的使用之上。
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.