This article is cited in 5 papers

Removable singularities of solutions of second-order divergence-form elliptic equations

A. V. Pokrovskii

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Let $L$ be a uniformly elliptic linear second-order differential operator in divergence form with bounded measurable coefficients in a bounded domain $G\subset\mathbb R^n$ $(n\geqslant2)$. In this paper, we introduce subclasses of the Sobolev class $W^{1,2}(G)_{\text{loc}}$ containing generalized solutions of the equation $Lu=0$ such that the closed sets of nonisolated removable singular points for such solutions can be described completely in terms of Hausdorff measures.

UDC: 517.956

Received: 17.10.2003

DOI: 10.4213/mzm2503

 English version: Mathematical Notes, 2005, 77:3, 391–399

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