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We study renormalized solutions to the problem $$\begin{align*} \begin{cases} -\Delta_pu=0 & \mbox{ in } \left\lbrace x \in \mathbb{R}^N : \left\lvert {x} \right\rvert>1\right\rbrace \\ \left\lvert {\nabla u} \right\rvert^{p-2}u_\nu + g(u) = \mu & \mbox{ on } \left\lbrace x \in \mathbb{R}^N : \left\lvert {x} \right\rvert=1\right\rbrace \end{cases} \end{align*} $$ { − Δ p u = 0 in { x ∈ R N : | x | > 1 } | ∇ u | p − 2 u ν + g (u) = μ on { x ∈ R N : | x | = 1 } where 1

From a unique viewpoint, singular elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms are investigated in cylindrical domains. The weight Neumann condition is set on the lateral area of the cylinder; no condition is set on the base of the cylinder (regardless the type of the equation). Results of two kinds are established: the existence of a limit of each solution (if it exists) along the axis of the cylinder and sufficient conditions of a blow-up (including instant or complete one). [ABSTRACT FROM AUTHOR]