Geodesic
On removability of singularities on manifolds for solutions of non-linear
Sbornik. Mathematics, Tome 194 (2003) no. 9, pp. 1361-1381

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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. 
@article{SM_2003_194_9_a3,
     author = {I. I. Skrypnik},
     title = {On removability  of  singularities on  manifolds for solutions of  non-linear},
     journal = {Sbornik. Mathematics},
     pages = {1361--1381},
     publisher = {mathdoc},
     volume = {194},
     number = {9},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_9_a3/}
}
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I. I. Skrypnik. On removability  of  singularities on  manifolds for solutions of  non-linear. Sbornik. Mathematics, Tome 194 (2003) no. 9, pp. 1361-1381. http://geodesic.mathdoc.fr/item/SM_2003_194_9_a3/