Abstract
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.
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