Del Teso Méndez, FélixLindgren, Erik2023-06-222023-06-2220220885-747410.1007/s10915-021-01745-zhttps://hdl.handle.net/20.500.14352/71302CRUE-CSIC (Acuerdos Transformativos 2021)We propose a new monotone finite difference discretization for the variational p-Laplace operator, pu = div(|∇u|p−2∇u), and present a convergent numerical scheme for related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson and one explicit method. Finally, we exhibit some numerical simulations supporting our theoretical results. To the best of our knowledge, this is the first monotone finite difference discretization of the variational p-Laplacian and also the first time that nonhomogeneous problems for this operator can be treated numerically with a finite difference scheme.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttps://doi.org/10.1007/s10915-021-01745-zopen accessp-LaplacianFinite differenceMean value propertyNonhomogeneous Dirichlet problemViscosity solutionsDynamic programming principleAnálisis matemático1202 Análisis y Análisis Funcional