Criteria for C-1-approximability of functions on compact sets in R-N, N = 3, by solutions of second-order homogeneous elliptic equations

We obtain capacitive criteria for the approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients in the norm of a Whitney-type C-1-space on a compact set in R-N, N >= 3. The case N = 2 was studied in a recent paper by the author and Tolsa. For C-1-approximations by harmonic functions (with any N), weaker criteria were earlier found by the author. We establish some metric properties of the capacities considered.