Efficient algorithms for solving the p-Laplacian in polynomial time

The p-Laplacian is a nonlinear partial differential equation, parametrized by $$p \in [1,\infty ]$$ p ∈ [ 1 , ∞ ] . We provide new numerical algorithms, based on the barrier method, for solving the p-Laplacian numerically in $$O(\sqrt{n}\log n)$$ O ( n log n ) Newton iterations for all $$p \in [1,\infty ]$$ p ∈ [ 1 , ∞ ] , where n is the number of grid points. We confirm our estimates with numerical experiments.