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For q , γ > 0 , we study existence and regularity of solutions for unbounded elliptic problems whose simplest model is − div 1 + u q ∇ u = f / u γ in Ω u = 0 on ∂ Ω , where f ∈ L m Ω , m ≥ 1. [ABSTRACT FROM AUTHOR]

In this work, we are concerned with a class of elliptic problems with both absorption terms and critical growth in the gradient. We suppose that the data belong to Lm() with m > n/2 and we prove the existence of bounded weak solutions via L1-estimates. A priori estimates and Stampacchia's L1-regularity are our main ingredient. [ABSTRACT FROM AUTHOR]

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 00 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation. [ABSTRACT FROM AUTHOR]