Existence of solutions to some elliptic system in Sobolev spaces with the weight as a power of the distance from some axis

Abstrakt

We examine some overdetermined elliptic system in a domain in $\mathbb R^3$ which contains an axis. Assuming that data functions belong to Sobolev spaces with weights equal to a power of the distance from the axis we prove existence of solutions in the corresponding kind of weighted Sobolev spaces.