Two problems on approximation by solutions of elliptic systems on compact sets in the plane

Nevanlinna domains with large boundaries

“…J. Verdera [34] formulated the following conjecture: if X is an arbitrary compact subset of the complex plane and if f is continuous on X and bianalytic on its interior, then f can be approximated uniformly on X by bianalytic rational functions without singularities in X. Omitting here the reasons supporting this conjecture (an appropriate discussion can be found in [34]) let us mention that it was proved recently by M. Mazalov [24]. Later on this result was generalized to the solutions of general elliptic equations with constant complex coefficients and locally bounded fundamental solutions in [25] (see also [18] for yet more observations concerning the matter).…”