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

Abstract

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.