On the Range of Ural’tseva’s Axially Symmetric Operator in Sobolev Spaces

In [9], N. Ural’tseva considered the second-order axially symmetric partial differential operator, which in our notations reads 1 L α : = α Δ + ( 1 − 3 α ) ∑ 1 2 i j x i x j ( x 1 2 + x 2 2 ) − 1 ∂ 2 / ∂ x i ∂ x j https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203744369/d9858e60-9246-4876-bb34-38e3d28ecc5f/content/eq49.tif"/>