Genival da Silva

An equation involving the 1-Laplacian and a singular nonlinearity

Abstract We prove existence of solutions to a nonlinear degenerate elliptic equation of the form $$ {\left\{ \begin{array}{ll} -\Delta _{1} u+ \frac{|D u|}{(1-u)^{\gamma }}=g & \hbox {in } \Omega ,\\ u=0 & \text{ on } \partial \Omega , \end{array}\right. } $$ - Δ 1 u + | D u | (...