On metric properties of $C$-capacities associated with solutions of second-order strongly elliptic equations in $\pmb{\mathbb R}^2$

For certain capacities that were used previously to formulate criteria for the uniform approximability of functions by solutions of strongly elliptic equations of the second order on compact subsets of $\mathbb R^2$, a number of metric properties are established. New, more natural criteria for individual approximability are obtained as consequences. Unsolved problems of interest are stated.
Bibliography: 13 titles.