Erratum to: Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications

Abstract

We have established Adams-type inequality for biharmonic operator on Heisenberg group and proved the existence of solution to a biharmonic equation involving a singular potential and a nonlinearity satisfying critical and subcritical exponential growth condition. We observed that there is a technical mistake in the homogeneous dimension of the Heisenberg group that is under consideration. For our results to be meaningful, we need to work with bounded domains in H1 instead of bounded domains in H4. The reason of this change is as follows: Let Ω ⊆ Hn be a bounded domain and Q = 2n + 2 be homogeneous dimension of Hn. When Q > 4 (n > 1), we know that D2,2 0 (Ω) → Lq(Ω), 1 ≤ q ≤ 2Q Q−4 . In the critical case, Q = 4(n = 1), D2,2 0 (Ω) → L∞(Ω). Then it is natural to ask, what is the best possible space for this embedding? To answer this question, we need an Adams-type inequality with Q = 4. Thus, we need to work with H1 instead of H4 in [1]. For the sake of clarity, we restate the main results of [1]. However, all the proofs remain unchanged.