On the Unique Continuation Properties for Elliptic Operators with Singular Potentials

Let u be a solution to a second order elliptic equation with singular potentials belongingto Kato-Fefferman-Phong’s class in Lipschitz domains.An elementary proof of the doubling propertyfor u~2 over balls is presented,if the balls are contained in the domain or centered at some points nearan open subset of the boundary on which the solution u vanishes continuously.Moreover,we provethe inner unique continuation theorems and the boundary unique continuation theorems for the ellipticequations,and we derive the Bweight properties for the solution u near the boundary.