Schrodinger operators with Leray-Hardy potential singular on the boundary

We study the kernel function of the operator u (sic) L(mu)u = -Delta u + mu/vertical bar x vertical bar(2)u in a bounded smooth domain Omega subset of R-+(N) such that 0 epsilon partial derivative Omega, where mu >= - N-2/4 is a constant. We show the existence of a Poisson kernel vanishing at 0and a singular kernel with a singularity at 0. We prove the existence and uniqueness of weak solutions of L(mu)u = 0 in Omega with boundary data nu + k delta(0), where nu is a Radon measure on partial derivative Omega\{0}, k epsilon R and show that this boundary data corresponds in a unique way to the boundary trace of positive solution of L(mu)u = 0 in Omega. (C) 2020 Elsevier Inc. All rights reserved.