ELLIPTIC OPERATORS WITH UNBOUNDED DIFFUSION COEFFICIENTS PERTURBED BY INVERSE SQUARE POTENTIALS IN Lp-SPACES

In this paper we give sufficient conditions on a >= 0 and c is an element of R ensuring that the space of test functions C-c(infinity) (R-N) is a core for the operator L(0)u = (1 + vertical bar x vertical bar(alpha))Delta u + c/vertical bar x vertical bar(2) u =: Lu + c/vertical bar x vertical bar(2) u and L-0 with a suitable domain generates a quasi-contractive and positivity preserving C-0-semigroup in L-p(R-N), 1 < p < infinity. The proofs are based on some L-p-weighted Hardy's inequality and perturbation techniques.