Semi-classical resolvent estimates for Schrödinger operators

We prove optimal resolvent estimates for self-adjoint operators of the form P(h)=(ih∇+b(x,h))²+V(x,h) on L²(Rⁿ), n≥3, where 0<h<<1 is a semi-classical parameter and the coefficients have very little regularity with respect to the radial variable only.