The Dirichlet problem for the 1-Laplacian with a general singular term and L 1 -data
Marta Latorre, Francescantonio Oliva, Francesco Petitta, Sergio Segura de León · Nonlinearity · 2021
Abstract We study the Dirichlet problem for an elliptic equation involving the 1-Laplace operator and a reaction term, namely: − Δ 1 u = h ( u ) f ( x ) in Ω , u = 0 on ∂ Ω , where Ω ⊂ R N is an open bounded set having Lipschitz boundary, f ∈ L 1 (Ω) is nonnegative, and h is a continuous real function that may possibly blow up at zero. We investigate optimal ranges for the data in order to obtain existence, nonexistence and (whenever expected) uniqueness of nonnegative solutions.