Parabolic equation with a singular potential

We study the existence of a nonnegative generalized solution of an initial-boundary value problem for the heat equation with a singular potential in an arbitrary bounded domain Ω ? R ⁿ , n ≥ 3, containing the unit ball. We show that if the condition ∝ _Ω V ^n/2+s |x| ^s dx ≤ c _n is satisfied for some s ≥ 0 and c _n = c _n (n, s, Ω) > 0, then the problem in question has a nonnegative solution.