We prove the existence and uniqueness of an entropy solution for nonlinear anisotropic elliptic equations with Neumann homogeneous boundary value condition for L1-data. We prove first, by using minimization techniques, the existence and uniqueness of a weak solution when the data is bounded, and by approximation methods, we prove a result of existence and uniqueness of an entropy solution

existence; uniqueness; entropy solution; nonlinear anisotropic elliptic equations; Neumann homogeneous boundary value