A Finite Difference Method for the Variational p-Laplacian

Abstract We propose a new monotone finite difference discretization for the variational p -Laplace operator, $$\Delta _pu=\text{ div }(|\nabla u|^{p-2}\nabla u),$$ ? p u = div ( | ? - 2 ) , and present convergent numerical scheme related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson explicit method. Finally, we exhibit some simulations supporting our theoretical results. To best of knowledge, this first -Laplacian also time that nonhomogeneous problems operator can be treated numerically with scheme.