Techniques of constrained approximation are used to recover solutions to elliptic partial
differential equations from incomplete and corrupted boundary data. The approach involves
constructive computations in generalized Hardy spaces of functions whose real and
imaginary parts are related by formulae similar to the Cauchy–Riemann equations: these
spaces were recently introduced by Baratchart, Leblond, Rigat and Russ. A prime motivation
for this research is the modeling of plasma confinement in a tokamak reactor. Constructive
and numerical aspects are also discussed in detail.
