Revised regularity results for quasilinear elliptic problems driven by the Φ-Laplacian operator.

It is establish regularity results for weak solutions of quasilinear elliptic problems driven by the well known Φ -Laplacian operator given by - Δ Φ u = g (x , u) , in Ω , u = 0 , on ∂ Ω , where Δ Φ u : = div (ϕ (| ∇ u |) ∇ u) and Ω ⊂ R N , N ≥ 2 , is a bounded domain with smooth boundary ∂ Ω . Our work concerns on nonlinearities g which can be homogeneous or non-homogeneous. For the homogeneous case we consider an existence result together with a regularity result proving that any weak solution remains bounded. Furthermore, for the non-homogeneous case, the nonlinear term g can be subcritical or critical proving also that any weak solution is bounded. The proofs are based on Moser's iteration in Orlicz and Orlicz-Sobolev spaces. [ABSTRACT FROM AUTHOR]