A new proof for the equivalence of weak and viscosity solutions for the p-Laplace equation

الأصل · EN

In this paper, we give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the p-Laplace equation -(Duᵖ⁻²Du)=0 coincide. Our proof is more direct and transparent than the original one by Juutinen, Lindqvist and Manfredi jlm, which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the p-Laplace equation.