  We consider the semi-linear, defocusing wave equation $\partial_t^2 u -
\Delta u = -|u|^{p-1} u$ in $\mathbb{R}^d$ with $1+4/(d-1)\leq p < 1+4/(d-2)$.
We generalize the inward/outward energy theory and weighted Morawetz estimates
in 3D to higher dimensions. As an application we show the scattering of
solutions if the energy of initial data decays at a certain rate as $|x|
\rightarrow \infty$.
