  Newton potential for DGP brane-world scenario is examined when the extra
dimension is semi-infinite. The final form of the potential involves a
self-adjoint extension parameter $\alpha$, which plays a role of an additional
mass (or distance) scale. The striking feature of Newton potential in this
setup is that the potential behaves as seven-dimensional in long range when
$\alpha$ is nonzero. For small $\alpha$ there is an intermediate range where
the potential is five-dimensional. Five-dimensional Newton constant decreases
with increase of $\alpha$ from zero. In the short range the four-dimensional
behavior is recovered. The physical implication of this result is discussed in
the context of the accelerating behavior of universe.
