Behaviour of solutions to <i>p</i>-Laplacian with Robin boundary conditions as <i>p</i> goes to 1

We study the asymptotic behaviour, as $p\to 1^+$ , of solutions following inhomogeneous Robin boundary value problem: P \begin{equation*} \begin{cases} \displaystyle -\Delta_p u_p = f &amp; \text{ in }\Omega,\\ |\nabla u_p|^{p-2}\nabla u_p\cdot \nu +\lambda |u_p|^{p-2}u_p g on } \partial\Omega, \end{cases} \end{equation*} where $\Omega$ is a bounded domain $\mathbb {R}^{N}$ with sufficiently smooth boundary, $\nu$ its unit outward normal vector and $\Delta _p v$ $p$ -Laplacian operator $p&gt;1$ . The data $f\in L^{N,\infty }(\Omega )$ (which denotes Marcinkiewicz space) $\lambda,\,g$ are functions defined $\partial \Omega$ $\lambda \ge 0$ find threshold below which family –solutions goes to 0 above this blows up. As second interest we deal $1$ problem formally arising by taking (P).