The membership of solutions of quasielliptic equations to space $L_p$

It is established that the solutions of a quasielliptic equation, belonging to space $L_1$ with weight equal to a negative power of the distance to the flat part of the boundary, belong to space $L_p$ with some $p>1$. In particular, the positive solutions of uniformly elliptic equations in bounded regions $\Omega$ with a smooth boundary belong to $L_p(\Omega)$ with any $p<n/(n-1)$, where $n$ is the dimension of the space of independent variables.