Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces

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.
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Advances in Pure and Applied Mathematics, De Gruyter, 2010, 2 (1), pp.47-63. 〈10.1515/apam.2010.026〉
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Contributeur : Juliette Leblond <>
Soumis le : lundi 11 mars 2013 - 11:28:40
Dernière modification le : vendredi 12 janvier 2018 - 11:03:35

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Yannick Fischer, Juliette Leblond. Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces. Advances in Pure and Applied Mathematics, De Gruyter, 2010, 2 (1), pp.47-63. 〈10.1515/apam.2010.026〉. 〈hal-00798959〉

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