Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply-connected domains

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.