Is there any result for the 4th order elliptic pde,like we do have for 2nd order pde: Consider the equation,\ $\Delta^2 u = a(x)u$ and $a(x)\in L^{\frac{n}{4}}(\Omega)$, where $\Omega$ is bounded. If $u \in H^2(\Omega)$ is a weak solution of the above equation Then we have $u \in L^q(\Omega)$ for any $1 \leq q <\infty$. [Or it may hold locally.]