Criteria for -approximability of functions on compact sets in , , by solutions of second-order homogeneous elliptic equations

Abstract

Abstract 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 -space on a compact set in , . The case was studied in a recent paper by the author and Tolsa. For -approximations by harmonic functions (with any ), weaker criteria were earlier found by the author. We establish some metric properties of the capacities considered.