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

Wojciech M. Zajączkowski
2002 Topological Methods in Nonlinear Analysis  
We examine some overdetermined elliptic system in a domain in 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. 2000 Mathematics Subject Classification. 35F15, 35N05.
doi:10.12775/tmna.2002.006 fatcat:5njwgwyvura35drlo7l4auhnq4