Resolvent bounds for Lipschitz potentials in dimension two and higher with singularities at the origin.

We consider, for h,E>0, the semiclassical Schrödinger operator -h²Δ+V-E in dimension two and higher. The potential V, and its radial derivative $\dell_{r}V$ are bounded away from the origin, have long-range decay and V is bounded by r-δ near the origin while $\dell_{r}V$ is bounded by r-1-δ, where 0≤δ≤4(2-√-1). In this setting, we show that the resolvent bound is exponential in h-1, while the exterior resolvent bound is linear in h-1. [ABSTRACT FROM AUTHOR]