  In 2012, F.Leonetti and F.Siepe [1] considered solutions to boundary value
problems of some anisotropic elliptic equations of the type $$ \left\{
\begin{array}{llll} \sum\limits _{i=1}\limits^{n} D_i (a_i(x,Du(x)))=0, &x\in
\Omega,\\ u(x)=\theta (x), & x\in \partial \Omega. \end{array} \right. $$ Under
some suitable conditions, they obtained an integrability result, which shows
that, higher integrability of the boundary datum $\theta$ forces solutions $u$
to have higher integrability as well. In the present paper, we consider ${\cal
K}_{\psi,\theta}^{(p_i)}$-obstacle problems of the nonhomogeneous anisotropic
elliptic equations $$ \sum_{i=1}^n D_i (a_i(x,Du(x)))=\sum_{i=1}^n D_i f^i(x).
$$ Under some controllable growth and monotonicity conditions. We obtain an
integrability result, which can be regarded as a generalization of the result
due to Leonetti and Siepe.
