In the previous work Hamamoto (Calc Var Partial Differ Equ 58(4):23, 2019), following from an idea of Costin–Maz’ya (Costin and Maz’ya in Calc Var Partial Differ Equ 32(4):523–532, 2008), we computed the best constant in Rellich–Leray inequality for axisymmetric solenoidal fields, including any radial power weight. In the present paper, we recompute it without such a symmetry assumption. As a result, it turns out that the best constant in the same inequality for solenoidal fields is distinct from the one for unconstrained fields, only when the weight exponent stays within a bounded range.

在上一个作品Hamamoto（Calc Var Partial Differ Equ 58（4）：23，2019）中，遵循Costin–Maz'ya的构想（Calc Var和Partial Differ Equ 32（4）：523–Costin和Maz'ya） 532，2008），我们针对轴对称螺线管场（包括任何径向功率权重）计算了Rellich-Leray不等式的最佳常数。在本文中，我们在没有这种对称性假设的情况下重新计算了它。结果，只有在权重指数保持在一定范围内时，电磁场在相同不等式中的最佳常数才与无约束场中的最佳常数不同。