I have seen a lemma which I do not have any reference or hint for it.

Assume $ \Omega \subset \mathbb{R^N} $ is smooth bounded domain and let $u$ be a positive distributional supersolution to \begin{cases} \Delta^2 u = 0 \hspace{.9cm} \mathrm{in} \hspace{.1cm} Ω \\ u =-\Delta u= 0 \hspace{.9cm} \mathrm{on} \hspace{.1cm} ∂Ω \end{cases} then for any $B_R(x_0) ⊂⊂ Ω $, there exists a positive constant $C = C(θ, ρ, q,R)$ , $0 <q< \dfrac{N}{ N−2}$ , $0 <θ<ρ< 1$ , such that

$$||u||_{L^q(B_{ρR}(x_0))} \leq C \hspace{.2cm} ess \inf_{B_{θR}(x_0)}u$$

I need a reference or hint, or any help to prove it.

Thanks.