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

Abstract

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