In [2] Kenig, Ruiz and Sogge proved$${\parallel u\parallel }_{L^{\frac{2n}{n-2}}\left({ℝ}^n\right)}\lesssim {\parallel Lu\parallel }_{L^{\frac{2n}{n+2}}\left({ℝ}^n\right)}$$provided $n\ge 3$, $u\in C_0^{\infty }\left({ℝ}^n\right)$ and $L$ is a second order operator with constant coefficients such that the second order coefficients are real and nonsingular. As a consequence of [3] we state local versions of this inequality for operators with $C^2$ coefficients. In this paper we show how to apply these local versions to the absence of embedded eigenvalues for potentials in $L^{\frac{n+1}{2}}$ and variants thereof.