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Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces
-
Y. Fischer
and
J. Leblond
Published/Copyright:
May 7, 2010
Abstract
We present a constructive method for the robust approximation to solutions of some elliptic equations in a plane domain from incomplete and corrupted boundary data. We state this inverse problem in generalized Hardy spaces of functions satisfying the conjugate Beltrami equation, of which we give some properties, in the Hilbertian framework. The issue is then reworded as a constrained approximation (bounded extremal) problem which is shown to be well-posed. A practical motivation comes from modelling plasma confinement in a tokamak reactor. There, the particular form of the conductivity coefficient leads to Bessel-exponential type families of solutions of which we establish density properties.
Received: 2009-12-04
Revised: 2010-03-12
Published Online: 2010-05-07
Published in Print: 2011-January
© de Gruyter 2010
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Articles in the same Issue
- Weighted Lp-solutions on unbounded intervals of nonlinear integral equations of the Hammerstein and Urysohn types
- Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
- Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces
- Toeplitz operators with L1 symbols on Bergman spaces in the unit ball of
- On the boundedness of pseudo-differential operators associated with the Dunkl transform on the real line
- Equivalences induced by n-self-cotilting comodules
