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We deal with existence and uniqueness of nonnegative solutions to:−Δu=f(x),inΩ,∂u∂ν+λ(x)u=g(x)uη,on∂Ω,\left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}&amp; \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial \nu }+\lambda \left(x)u=\frac{g\left(x)}{{u}^{\eta }},\hspace{1.0em}&amp; \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial \Omega ,\end{array}\right.whereη≥0\eta \ge 0andf,λf,\lambda, andggare the nonnegative integrable functions. The setΩ⊂RN(N&gt;2)\Omega \subset {{\mathbb{R}}}^{N}\left(N\gt 2)is open and bounded with smooth boundary, andν\nudenotes its unit outward normal vector. More generally, we handle equations driven by monotone operators ofpp-Laplacian type jointly with nonlinear boundary conditions. We prove the existence of an entropy solution and check that, under natural assumptions, this solution is unique. Among other features, we study the regularizing effect given to the solution by both the absorption and the nonlinear boundary term.

On a nonlinear Robin problem with an absorption term on the boundary and L 1 data