The associated primes of local cohomology modules over rings of small dimension

Let R be a commutative Noetherian local ring of dimension d, I an ideal of R, and M a finitely generated R-module. We prove that the set of associated primes of the local cohomology module H-I(i)(M) is finite for all i greater than or equal to0 in the following cases: (1)d less than or equal to3; (2) d = 4 and R is regular on the punctured spectrum; (3)d = 5, R is an unramified regular local ring, and M is torsion-free. In addition, if d > 0 then H-I(d-1) (M) has finite support for arbitrary R, I, and M.