Abstract:Let $F$ be a relatively closed subset of a Euclidean domain $\Omega $. We investigate when solutions $u$ to certain elliptic equations on $\Omega \setminus F$ are restrictions of solutions on all of $\Omega $. Specifically, we show that if $\partial F$ is not too large, and $u$ has a suitable decay rate near $F$, then $u$ can be so extended.
Keywords: $\Cal A$-harmonic function, Hausdorff measure, Fusion problem
AMS Subject Classification: 35J60, 28A78