On the continuity of solutions to the anisotropic N-Laplacian with L¹ lower order term

We establish the continuity of bounded solutions to the anisotropic elliptic equation aligned -∑ ᵢ₌₁N (|uxᵢ|pᵢ-2 uxᵢ )xᵢ=f(x), x∈ Ω , f(x)∈ L¹(Ω ) aligned under the conditions aligned min 1 i N pᵢ >1, ∑ ᵢ₌₁N 1/pᵢ=1 aligned and aligned lim ρ → 0\, x∈ Ω∫ ρ₀ (∫ Bᵣ(x)|f(y)|\,dy )1/N-1dr/r=0. aligned In the standard case p₁=...=pN=N , these conditions recover the known results for the N -Laplacian.