Abstract:
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.
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