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

A. V. Pokrovskii

Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 424-433.

Résumé

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.

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