Given p > 1 p > 1 , let u u be a solution to div ⁡ ( ∇ u | p − 2 ∇ u ) = 0 \operatorname {div}(\nabla u{|^{p - 2}}\nabla u) = 0 , on a domain Ω \Omega of the plane. Using the theory of quasiregular mappings we prove that the zeros of ∇ u \nabla u are isolated in Ω \Omega , obtain bounds for the Hölder exponent of ∇ u \nabla u and prove a strong form of the comparison principle.