Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation

Abstract

We study the relation between viscosity solutions and weak solutions of the equation $${\partial }_t\left(|u{|}^{p-2}u\right)=\mathrm{div}(|\nabla u{|}^{p-2}\nabla u).$$ We prove that at least for non-negative functions these are equivalent concepts.