Existence of solutions to some elliptic system in Sobolev spaces with the weight as a power of the distance from some axis - Zajączkowski, Wojciech M. (Topological Methods in Nonlinear Analysis, 2002)
We examine some overdetermined elliptic system in a domain in $\mathbb R^3$ whichcontains an axis. Assuming that data functions belong to Sobolev spaces withweights equal to a power of the distance from the axis we prove existence ofsolutions in the corresponding kind of weighted Sobolev spaces.