On Carlson's type removability test for the degenerate quasilinear elliptic equations (Q762910)

Summary: A Carlson's type theorem on removable sets for \(\alpha\)-Hölder continuous solutions is investigated for the quasilinear elliptic equations \(\text{div}A(x, u, \nabla u) = 0\), having degeneration \(\omega\) in the Muckenhoupt class. In particular, when \(\alpha\) is sufficiently small and the operator is a weighted \(p\)-Laplacian, we show that the compact set \(E\) is removable if and only if the Hausdorff measure \(\Lambda^{-p+(p-1)\alpha}_\omega(E) = 0\).