On Carlson's Type Removability Test for the Degenerate Quasilinear Elliptic Equations

Abstract EN

Carlson's type theorem on removable sets for α-Holder continuous solutions is investigated for the quasilinear elliptic equations div A(x,u,∇u)=0, having degeneration ω in the Muckenhoupt class.

In partial, when α is sufficiently small and the operator is weighted p-Laplacian, we show that the compact set E is removable if and only if the Hausdorff measure Λω−p+(p−1)α(E)=0.