0x69410865

Consider the setup in (0x67dbeaae) .

Employing the estimates (0x68dcfef9) and (0x68bbccca) , yields that there is constant depending on \(d\), such that

\begin{equation*} \lVert \nabla^k u\rVert_{L^2(\mathbb{S}^d_{R})}^2 \le C^k (E^k + R^{-2k} (k!)^2)). \end{equation*}

This estimate is applicable in Kovrijkine’s Lemma if the radius in the expansion is small enough.