Uniform approximation of functions by solutions of strongly elliptic equations of second order on compact subsets of $\mathbb R^2$

Criteria for the uniform approximation of functions by solutions of second-order strongly elliptic equations on compact subsets of $\mathbb R^2$ are obtained using the method of reduction to similar problems in $\mathbb R^3$, which were previously investigated by Mazalov. A number of metric properties of the capacities used are established.
Bibliography: 16 titles.