© 2018, Springer Nature Switzerland AG. Criteria for approximability of functions by solutions of homogeneous second order elliptic equations (with constant complex coefficients) in the norms of the Whitney C1-spaces on compact sets in R2 are obtained in terms of the respective C1-capacities. It is proved that the mentioned C1-capacities are comparable to the classic C-analytic capacity, and so have a proper geometric measure characterization.
- C-analytic capacity
- C -approximation 1
- Curvature of measure
- LC -capacity 1
- Localization operator of Vitushkin type
- Second order homogeneous elliptic operator