The Yamabe Problem for Distributional Curvature

In this paper, we consider Yamabe problem for a smooth manifold with a W-1,W-p metric. The curvature is considered as a distribution since our metric is not twice differentiable. We prove that for any metric g which is W-1,W-p on M such that the Yamabe constant of (M, g) is less than that of the standard sphere, there exists a W-1,W-p metric on M which is conformal to g and has constant distributional scalar curvature.