Dirichlet Parabolic Problems Involving Schrodinger Type Operators with Unbounded Diffusion and Singular Potential Terms in Unbounded Domains

We study the well-posedness of autonomous parabolic Dirichlet problems involving Schrodinger type operators of the form H-alpha,H-a,H-b,H-c = (1 + vertical bar x vertical bar(alpha))Delta + a vertical bar x vertical bar(alpha) + b vertical bar x vertical bar(alpha-2) + c vertical bar x vertical bar(-2) , with alpha >= 0, and a < 0 and b, c is an element of R, in regular unbounded domains Omega subset of R-N containing 0. Under suitable assumptions on alpha, b and c, the solution is governed by a contractive and positivity preserving strongly continuous (analytic) semigroup on the weighted space L-p(Omega, d mu(x)), 1 < p < infinity, where d mu(x) = (1 + vertical bar x vertical bar(alpha))(-1) dx. The proofs are based on some L-p-weighted Hardy's inequality and perturbation techniques.