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

DOI: http://dx.doi.org/10.12775/TMNA.2002.006

#### Abstract

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.

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.

#### Keywords

elliptic boundary value problem; bounded domain; existence; weighted Sobolev spaces

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