4 papers
First Dirichlet eigenvalue of the weighted 1-Laplacian operator
R. Barbato, J. C. Sabina de Lis, S. Segura de León
In this paper, we study the eigenvalue problem \[\left\{\begin{array}{cl}-\hbox{div}\left(a(x)\frac{Du}{|Du|}\right)=Λ\, b(x)\frac{u}{|u|} & \text{in }Ω\\u=0 & \text{on }\partialΩ,…
Singular elliptic equations having a gradient term with natural growth
A. Ferone, A. Mercaldo, S. Segura de León
We study a class of Dirichlet boundary value problems whose prototype is \begin{equation}\label{1.2abs} \left\{\begin{array}{ll} -Δ_p u =h(u)|\nabla u|^p+u^{q-1}+f(x)\, &\quad\hbox…
On a nonlinear Robin problem with an absorption term on the boundary and data
Francesco Della Pietra, Francescantonio Oliva, Sergio Segura de León
We deal with existence and uniqueness of nonnegative solutions to \begin{equation*} \left\{ \begin{array}{l} -Δu = f(x) \text{ in }Ω, \frac{\partial u}{\partial ν} + λ(x) u = \frac…
Elliptic equations involving the 1--Laplacian and a total variation term with --data
M. Latorre, S. Segura de León
In this paper we study, in an open bounded set with Lipschitz boundary , the Dirichlet problem for a nonlinear singular elliptic equation involving…