This article is cited in 3 papers

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

I. I. Skrypnik

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

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.

UDC: 517.946

MSC: Primary 35J60; Secondary 35B60

Received: 24.01.2003

DOI: 10.4213/sm768

 English version: Sbornik: Mathematics, 2003, 194:9, 1361–1381

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