Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply-connected domains
نویسندگان
چکیده
Techniques of constrained approximation are used to recover solutions to elliptic partial differential equations from incomplete and corrupted boundary data. The approach involves the use of generalized Hardy spaces of functions whose real and imaginary parts are related by formulae similar to the Cauchy–Riemann equations. A prime motivation for this is the modelling of plasma confinement in a tokamak reactor. Constructive and numerical aspects are also discussed. Key-words: Hardy classes, extremal problems, inverse Dirichlet-Neumann problems ∗ INRIA Sophia Antipolis Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France, [email protected], [email protected] † School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K., [email protected] in ria -0 04 60 82 0, v er si on 3 9 Ju n 20 10 Problèmes extrémaux bornés dans des espaces de Hardy pour l’équation de Beltrami conjuguée dans des domaines simplement connexes Résumé : Des techniques d’approximation sous contraintes sont mises en oeuvre pour retrouver les solutions d’une equation aux dérivées partielles elliptique à partir de données incomplètes et bruitées disponibles sur le bord du domaine d’étude. Cette approche nécessite l’utilisation de fonctions dans des espaces de Hardy généralisés dont les parties réelles et imaginaires sont reliées par des formules analogues aux équations de Cauchy-Riemann. Une importante motivation pour ce travail concerne la modélisation du confinement d’un plasma au sein d’un tokamak. Les aspects constructifs et numeriques seront par ailleurs examinés. Mots-clés : classes de Hardy, problèmes extrémaux, problèmes inverses Dirichlet-Neumann in ria -0 04 60 82 0, v er si on 3 9 Ju n 20 10 Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation 3
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