On the behaviour of the first eigenvalue of the $p$-Laplacian with Robin boundary conditions as $p$ goes to $1$

Francesco Della Pietra, Carlo Nitsch, Francescantonio Oliva +1

In this paper we study the $\Gamma$-limit, as $p\to 1$, of the functional $$J_p(u)=\frac{{\int }_{\Omega }|\nabla u{|}^p+\beta {\int }_{\partial \Omega }|u{|}^p}{{\int }_{\Omega }|u{|}^p},$$ w…