  Criteria for approximability of functions by solutions of homogeneous second
order elliptic equations (with constant complex coefficients) in the norms of
the Whitney $C^1$-spaces on compact sets in $\mathbb R^2$ are obtained in terms
of the respective $C^1$-capacities. It is proved that the mentioned
$C^1$-capacities are comparable to the classic $C$-analytic capacity, and so
have a proper geometric measure characterization.
