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I'm sorry I ignore the condition of $a_{ij}$, but there is a Moser's iteration for $-\Delta u + V(x)u=0$. It says that if $V\in L^{\frac{q}{2}}(\Omega)$ for some $q>n$, then $u\in L^{\infty}(\Omega)$. For instance, see Struwe's Variational Methods Appendix B lemma B.3. And I think this iteration doesn't need the continuous of $a$.