Anisotropic Elliptic Equations in L^m

We prove the existence of solutions to anisotropic nonlinear elliptic equations with right hand side term in $L^m(\Omega)$ and obtain the appropriate function space for the weak solutions. This paper gives a generalization of some results given by L. Boccardo, T. Gallouet and P. Marcellini [Diff. Integral Equations 9 (1996) 209–212] and by L. Boccardo and T. Gallouet [Comm. Partial Diff. Equations 17 (1992) 641–655].