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

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.

Keywords


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

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