Local behavior of solutions of the stationary Schr\" odinger equation   with singular potentials and bounds on the density of states of   Schr\"{o}dinger operators
  We study the local behavior of solutions of the stationary Schr\" od\-inger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this result with a quantitative unique continuation principle for singular potentials we obtain log-H\"older continuity for the density of states outer-measure in one, two, and three dimensions for Schr\" odinger operators with singular potentials, results that hold for the density of states measure when it exists. 
Abel Klein and C.S. Sidney Tsang
math.AP