Parabolic theory of the discrete pp-Laplace operator

We study the discrete version of the pp-Laplace operator. Based on its variational properties we discuss some features of the associated parabolic problem. We prove well-posedness of the problem and obtain information about positivity and comparison principles as well as compatibility with the symmetries of the underlying graph. Our methods consist in an interplay of the theory of subdifferentials and of combinatorial methods. We conclude briefly discussing the variational properties of a handful of nonlinear generalized Laplacians appearing in different parabolic equations.