On removability of singularities on manifolds for solutions of non-linear elliptic equations

A precise condition is found for the removability of a singularity on a smooth manifold for solutions of non-linear second-order elliptic equations of divergence form. The condition is stated in the form of a dependence of the pointwise behaviour of the solution on the distance to the singular manifold. The condition obtained is weaker than Serrin's well-known sufficient condition for the removability of a singularity on a manifold.