A Rado type theorem for p-harmonic functions in the plane

Abstract

We show that if u ∈ C1(Ω) satisfies the p-Laplace equation div(|∇u|p−2∇u) = 0 in Ω \ {x : u(x) = 0}, then u is a solution to the p-Laplacian in the whole Ω ⊂ R2.