Removable singularities for solutions of second-order linear uniformly elliptic equations in non-divergence form

A. V. Pokrovskii

Sbornik. Mathematics, Tome 199 (2008) no. 6, pp. 923-944

Résumé

Let $\mathfrak L$ be a linear uniformly elliptic operator of the second order in $\mathbb R^n$, $n\geqslant2$, with bounded measurable real coefficients, that satisfies the weak uniqueness property. The removability of compact subsets of a domain $D\subset\mathbb R^n$ is studied for weak solutions of the equation $\mathfrak Lf=0$ (in the sense of Krylov and Safonov) in some classes of continuous functions in $D$. In particular, a metric criterion for removability in Hölder classes with small exponent of smoothness is obtained. Bibliography: 20 titles.